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Gaussian Elimination
Let’s consider a problem where we have to buy oranges and apples but under the following conditions. The difference between 2X the number of oranges and the number of apples should be 3. The sum of 4X the number of oranges and the number of apples should be 9. The difference between 5X the number of oranges and 3X the number of apples should be 7. System of Linear Equations These conditions could be modeled using the following equations...
Matrices
A matrix is a rank 2 tensor i.e. an array expanding in a maximum of two independent dimensions. Multiple vectors could be arranged in rows or columns to create a matrix. $$\vec{a} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}\ \ \vec{b} = \begin{bmatrix} 7 \\ 9 \\ 10 \end{bmatrix}$$ $$\textbf{A} = \begin{bmatrix} \vec{a} & \vec{b} \end{bmatrix} = \begin{bmatrix} 5 & 7 \\ 6 & 9 \\ 7 & 10 \end{bmatrix}$$...
Vectors
A vector could represent the magnitude of a quantity broken down into its various components, for example, the velocity of an object moving on a 2D plane could be represented using the vector $\vec{v} = \begin{bmatrix} 8 & 9 \end{bmatrix}$. On a 2D plane $8$ and $9$ could be called the horizontal and vertical components of the vector $\vec{v}$ respectively. But the words horizontal and vertical on a 2D or 3D plane are relative to the viewer (try rotating the figure above anti-clockwise)....
Tensors
In linear algebra, a tensor is an array of data expanding in multiple (or zero) independent dimensions. It is used to represent quantities/equations/functions with multiple components, for example, the equation $3x+2y=0$ could be represented with the tensor $[3\ 2\ 0]$ where each value in the tensor represents the different components of the equation. The number of independent dimensions of a tensor is called its rank. Vectors and matrices could be generalized with the term tensor....
brag: A Command Line Tool for Building a Bragging Document
Inspired by Julia Evan’s blog Get your work recognized: write a brag document I created this tool to keep a record of my brags in Markdown Format and refer them later to create a formatted bragging document. A bragging or hype document is created to keep a record of achievements over time. This document/information extracted from this document could be shared with managers or used for self-reflection and improvement. I refer to it during my daily standups and weekly sync-up meetings....