From 830f1780ab1964cdc6678cf5bb10f7e60915e3c1 Mon Sep 17 00:00:00 2001 From: Karan Jayachandra Date: Sat, 18 Apr 2026 17:43:46 +0200 Subject: Removed the link to the Dutch certificate --- content/_index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'content') diff --git a/content/_index.md b/content/_index.md index 5198fa0..2919049 100644 --- a/content/_index.md +++ b/content/_index.md @@ -13,7 +13,7 @@ My Alma mater includes [TU Delft](https://microelectronics.tudelft.nl/Education/ ## My skills -The problems facing the world are constantly evolving. Being a generalist in such a dynamic situation is as asset. I have therefore strived to create a broad skill set. I have a basic understanding of how to write good software and am well versed in python and MATLAB development. I have some experience in C programming to accelerate algorithms using DSP processors. I have worked with FPGAs in the past using VHDL for prototyping but require time to refresh my skills. I aim to upskill on circuit design as well. I also know a bit of web development as you can see via this [website](https://gitlab.com/KaranJayachandra/karanjayachandra.gitlab.io) and a hobby project of mine called [match up](https://gitlab.com/KaranJayachandra/match_up). Web development helps me create tools that can be shared across a wider audience such a team in my organization. I would like to learn Erlang for concurrent applications and OCaml for functional programming in the future. Attending conferences inspires me. I have attended [EuRAD 2024](https://ieee-aess.org/event/conference/2024-21st-european-radar-conference) in Paris and [IRC2023](https://ieee-aess.org/event/conference/2023-ieee-international-radar-conference) in Sydney. I speak English and have a A1+ [certification](https://www.icloud.com/iclouddrive/084ABlGSRhK2lCny1UmqPxuXg#024_ste_language_dutch_a1_plus) in Dutch. I also speak four other Indian languages. +The problems facing the world are constantly evolving. Being a generalist in such a dynamic situation is as asset. I have therefore strived to create a broad skill set. I have a basic understanding of how to write good software and am well versed in python and MATLAB development. I have some experience in C programming to accelerate algorithms using DSP processors. I have worked with FPGAs in the past using VHDL for prototyping but require time to refresh my skills. I aim to upskill on circuit design as well. I also know a bit of web development as you can see via this [website](https://gitlab.com/KaranJayachandra/karanjayachandra.gitlab.io) and a hobby project of mine called [match up](https://gitlab.com/KaranJayachandra/match_up). Web development helps me create tools that can be shared across a wider audience such a team in my organization. I would like to learn Erlang for concurrent applications and OCaml for functional programming in the future. Attending conferences inspires me. I have attended [EuRAD 2024](https://ieee-aess.org/event/conference/2024-21st-european-radar-conference) in Paris and [IRC2023](https://ieee-aess.org/event/conference/2023-ieee-international-radar-conference) in Sydney. I speak English and have a A1+ certification in Dutch. I also speak four other Indian languages. ## About Me -- cgit v1.3.1 From b3194a1bef5062ed1304c7e68811656a1ce9f4ed Mon Sep 17 00:00:00 2001 From: Karan Jayachandra Date: Mon, 20 Apr 2026 08:52:33 +0200 Subject: Added the image to explain linear and affine transforms --- .gitignore | 5 +- content/_index.md | 3 - content/posts/linear_algebra.md | 33 --- content/posts/linear_algebra/index.md | 35 +++ content/posts/linear_algebra/matrices.ipe | 446 ++++++++++++++++++++++++++++++ content/posts/linear_algebra/matrices.svg | 440 +++++++++++++++++++++++++++++ static/main.css | 4 +- 7 files changed, 927 insertions(+), 39 deletions(-) delete mode 100644 content/posts/linear_algebra.md create mode 100644 content/posts/linear_algebra/index.md create mode 100644 content/posts/linear_algebra/matrices.ipe create mode 100644 content/posts/linear_algebra/matrices.svg (limited to 'content') diff --git a/.gitignore b/.gitignore index 07ed96b..a4c1a05 100644 --- a/.gitignore +++ b/.gitignore @@ -19,4 +19,7 @@ hugo.linux /.hugo_build.lock # Typst Output -resume.pdf \ No newline at end of file +resume.pdf + +# Ipe Autosaves +*.autosave.ipe \ No newline at end of file diff --git a/content/_index.md b/content/_index.md index 2919049..1c7a18c 100644 --- a/content/_index.md +++ b/content/_index.md @@ -2,9 +2,6 @@ Welcome to my home on the world wide web! I am a radio frequency (RF) engineer w ![profile](profile.jpg) -Signal Processing and Test Engineer -Systems and Applications - Algorithms, NXP - ## My journey I am currently working on the next generation of automotive Radar systems for applications like adaptive cruise control and lane change assist at [NXP](https://www.nxp.com). I have developed algorithms and built signal processing chains to estimate radar target parameters across 3 generations of radar prototypes. I have performed end-to-end testing of the developed systems using cutting-edge lab equipment and validated its performance in outdoor scenarios. I lead the development of team infrastructure for verification and validation of RF systems. In this role, I have helped speed up and standardize the testing process across multiple teams and projects. Before this I worked as a software consultant for three years at [SAP](https://www.sap.com/india/index.html). As a consultant I worked with diverse teams both within India and globally and delivered successful projects across multiple domains. At my tenure in SAP, I learnt how to manage stakeholders and create value for my team and company. This lead to multiple awards in recognition of my contributions. As an intern at [DRDO](https://www.indiascienceandtechnology.gov.in/organisations/ministry-and-departments/defence-research-and-development-organisation-drdo-govt-india/centre-artificial-intelligence-robotics-cair), I worked on a method of uniquely identify FPGA boards leveraging the randomness in silicon structure via ring oscillators. diff --git a/content/posts/linear_algebra.md b/content/posts/linear_algebra.md deleted file mode 100644 index 5239a97..0000000 --- a/content/posts/linear_algebra.md +++ /dev/null @@ -1,33 +0,0 @@ -+++ -title = "Essence of Linear Algebra" -date = 2026-04-14 -math = true -+++ - -When I first encountered linear algebra in school, I failed to realize the profound impact it has on the world around us. At this moment all I could think of was that this was a tool to solve $n$ equations in $n$ unknowns. This recurred when I was studying Linear Algebra although at a higher level during my undergraduate studies. When studying for my master's degree I saw the gaping hole in knowledge I had in basic mathematics. Things my fellow students found intuitive would require me to spend time writing several equations. It was at this point that I realized that I needed a refresher course. At this moment I came across [Gilbert Strang's Lectures for MIT18.06](https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PLE7DDD91010BC51F8). This was a godsend. Without this course I do not think I would have my degree or a job. I even wrote an email to this effect to Prof. Strang who was also kind enough to respond and warm greetings. I find his [book](https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html) on this topic to be the definitive source of information on Linear Algebra. No article can hope to capture the effect that attending his lectures would. I highly recommend that you do it if you have the time. However if you are in need of a quick recap of its concept, I summarize my understanding of the course in a way that made sense. It is more of a reference for myself for the future when I might forget a thing or two. Here we go! - -## Vectors - -The fundamental unit of linear algebra is a vector. A vector is a collection of numbers that belong together. The most basic of which you might be familiar with as the cartesian coordinate system where the numbers represent the components along the $x$, $y$ and $z$ axes. - -$$ \mathbf{v} = \begin{bmatrix} x \\\\ y \\\\ z \end{bmatrix} $$ - -But it doesn't have to be this literal. A vector can contain any information. A more realistic example could be a vector containing id of a car dealership, the number of sedans sold at the location, the total number of sales persons and the number of years the location has been active. Any set of related information can be added to a vector. Even words can be used by creating a numerical representation of it. This is what is done by LLMs. A vector is not limited in dimensions. The examples above have 3 and 4 dimensions or in mathematical terms in $\mathcal{R}^3$ and $\mathcal{R}^4$. But this can be extended to any random number of dimensions, $\mathcal{R}^n$. Vectors can be added together and scale. A linear combination is a generalization of combining vectors in different amounts. Notice that vectors are usually denoted in bold in mathematical notation. - -$$ \mathbf{y} = c_1 \mathbf{x}_1 + c_2 \mathbf{x}_2 + c_3 \mathbf{x}_3 $$ - -## Matrices - -A matrix is a useful way of representing a transformation. A matrix is a set of vector as described in the earlier section stacked together horizontally. Another way of thinking of a matrix is the transformation of reference axes. In 3 dimensions, the unit vector along the $x$, $y$ and $z$ axis is defined as $\begin{bmatrix} 1 & 0 & 0 \end{bmatrix}$, $\begin{bmatrix} 0 & 1 & 0 \end{bmatrix}$ and $\begin{bmatrix} 0 & 0 & 1 \end{bmatrix}$. If we stack these one top of each other, we arrive at the identity matrix or the default axes. We can transform these axes to point to any other directions by just stacking those vectors into a matrix and then multiplying them. Notice that the operation carried out is now just the dot product of the vector with axes that was just defined. The dot product is just a measure of how much the vector is pointing in the direction of another vector which in our case is the new axes. - -$$ \mathbf{v} = \begin{bmatrix} 1 & 2 & 3\\\\ 3 & 5 & 8 \\\\ 11 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\\\ y \\\\ z \end{bmatrix} = \begin{bmatrix} x + 2y + 3z \\\\ 3x + 5y + 8z \\\\ 11x + 3y + z \end{bmatrix} $$ - -This operation is another way of representing the linear transformation discussed in the previous section. I like to this of this operation as refocusing any and all vectors to a different section of space. This can be generalized with a change in the origin as well using the affine transformation written as: - -$$ \mathbf{y} = \mathbf{A} \mathbf{x} + \mathbf{b} $$ - -where $\mathbf{A}$ is the change in perspective and $\mathbf{b}$ is the change in point of reference. - -## Matrix Rank - -This section is to be continued. \ No newline at end of file diff --git a/content/posts/linear_algebra/index.md b/content/posts/linear_algebra/index.md new file mode 100644 index 0000000..dc52ef1 --- /dev/null +++ b/content/posts/linear_algebra/index.md @@ -0,0 +1,35 @@ ++++ +title = "Essence of Linear Algebra" +date = 2026-04-14 +math = true ++++ + +When I first encountered linear algebra in school, I failed to realize the profound impact it has on the world around us. At this moment all I could think of was that this was a tool to solve $n$ equations in $n$ unknowns. This recurred when I was studying Linear Algebra although at a higher level during my undergraduate studies. When studying for my master's degree I saw the gaping hole in knowledge I had in basic mathematics. Things my fellow students found intuitive would require me to spend time writing several equations. It was at this point that I realized that I needed a refresher course. At this moment I came across [Gilbert Strang's Lectures for MIT18.06](https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PLE7DDD91010BC51F8). This was a godsend. Without this course I do not think I would have my degree or a job. I even wrote an email to this effect to Prof. Strang who was also kind enough to respond and warm greetings. I find his [book](https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html) on this topic to be the definitive source of information on Linear Algebra. No article can hope to capture the effect that attending his lectures would. I highly recommend that you do it if you have the time. However if you are in need of a quick recap of its concept, I summarize my understanding of the course in a way that made sense. It is more of a reference for myself for the future when I might forget a thing or two. Here we go! + +## Vectors + +The fundamental unit of linear algebra is a vector. A vector is a collection of numbers that belong together. The most basic of which you might be familiar with as the cartesian coordinate system where the numbers represent the components along the $x$, $y$ and $z$ axes. + +$$ \mathbf{v} = \begin{bmatrix} x \\\\ y \\\\ z \end{bmatrix} $$ + +But it doesn't have to be this literal. A vector can contain any information. A more realistic example could be a vector containing id of a car dealership, the number of sedans sold at the location, the total number of sales persons and the number of years the location has been active. Any set of related information can be added to a vector. Even words can be used by creating a numerical representation of it. This is what is done by LLMs. A vector is not limited in dimensions. The examples above have 3 and 4 dimensions or in mathematical terms in $\mathcal{R}^3$ and $\mathcal{R}^4$. But this can be extended to any random number of dimensions, $\mathcal{R}^n$. Vectors can be added together and scale. A linear combination is a generalization of combining vectors in different amounts. Notice that vectors are usually denoted in bold in mathematical notation. + +$$ \mathbf{y} = c_1 \mathbf{x}_1 + c_2 \mathbf{x}_2 + c_3 \mathbf{x}_3 $$ + +## Matrices + +A matrix is a useful way of representing a transformation. A matrix is a set of vector as described in the earlier section stacked together horizontally. Another way of thinking of a matrix is the transformation of reference axes. In 3 dimensions, the unit vector along the $x$, $y$ and $z$ axis is defined as $\begin{bmatrix} 1 & 0 & 0 \end{bmatrix}$, $\begin{bmatrix} 0 & 1 & 0 \end{bmatrix}$ and $\begin{bmatrix} 0 & 0 & 1 \end{bmatrix}$. If we stack these one top of each other, we arrive at the identity matrix or the default axes. We can transform these axes to point to any other directions by just stacking those vectors into a matrix and then multiplying them. Notice that the operation carried out is now just the dot product of the vector with axes that was just defined. The dot product is just a measure of how much the vector is pointing in the direction of another vector which in our case is the new axes. + +$$ \mathbf{v} = \begin{bmatrix} 1 & 2 & 3\\\\ 3 & 5 & 8 \\\\ 11 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\\\ y \\\\ z \end{bmatrix} = \begin{bmatrix} x + 2y + 3z \\\\ 3x + 5y + 8z \\\\ 11x + 3y + z \end{bmatrix} $$ + +This operation is another way of representing the linear transformation discussed in the previous section. I like to this of this operation as refocusing any and all vectors to a different section of space. This can be generalized with a change in the origin as well using the affine transformation written as: + +$$ \mathbf{y} = \mathbf{A} \mathbf{x} + \mathbf{b} $$ + +where $\mathbf{A}$ is the change in perspective and $\mathbf{b}$ is the change in point of reference. + +![Matrix transformations](./matrices.svg) + +## Matrix Rank + +This section is to be continued. \ No newline at end of file diff --git a/content/posts/linear_algebra/matrices.ipe b/content/posts/linear_algebra/matrices.ipe new file mode 100644 index 0000000..a8a48c4 --- /dev/null +++ b/content/posts/linear_algebra/matrices.ipe @@ -0,0 +1,446 @@ + + + + +\usepackage{amsmath} + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +176 720 m +176 800 l +256 800 l +256 720 l +h + + +16 720 m +48 784 l +96 784 l +96 736 l +16 720 l + + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{x}_1 +\bf{x}_2 +\bf{x} + +80 736 m +104 800 l + + +80 736 m +136 764 l + +\bf{r}_2 +\bf{r}_1 + +16 720 m +84 804 l + +\bf{y} = \bf{A} \bf{x} + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 +\bf{y} = \begin{bmatrix} +\bf{r}_1 \cdot \bf{x}\\ +\bf{r}_2 \cdot \bf{x} +\end{bmatrix} + +40 784 m +96 784 l + + +96 784 m +96 736 l + + +128 720 m +176 768 l + + +112 752 m +160 752 l + + +176 720 m +176 800 l +256 800 l +256 720 l +h + + +176 720 m +176 800 l +256 800 l +256 720 l +h + +\bf{b} + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 +\bf{y} = \begin{bmatrix} +\bf{r}_1 \cdot \bf{x}\\ +\bf{r}_2 \cdot \bf{x} +\end{bmatrix} + +128 720 m +176 768 l + + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 + +272 720 m +272 720 l +288 752 l + +\bf{z} = \bf{y} + \bf{b} + +112 752 m +160 752 l + + +128 720 m +176 768 l + +\bf{z} + + diff --git a/content/posts/linear_algebra/matrices.svg b/content/posts/linear_algebra/matrices.svg new file mode 100644 index 0000000..22477b7 --- /dev/null +++ b/content/posts/linear_algebra/matrices.svg @@ -0,0 +1,440 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/static/main.css b/static/main.css index c698b25..2d0ad77 100644 --- a/static/main.css +++ b/static/main.css @@ -29,10 +29,10 @@ h1, h2, h3 { a { color: var(--theme-color); } -body img { +img { display: block; margin: auto; - max-width: 100%; + width: 100%; } nav ul, nav ol { padding: 0%; -- cgit v1.3.1