NAV Onboarding

nav_onboarding/README.md

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+## Navigation Onboarding
+
+Welcome to navigation!
+TODO: Add brief descritpion and simple rust excerises.
+
+## Basic Linear Algebra
+Make sure you are familiar with the following concepts:
+
+### Matrix Addition
+Matrix addition is performed element-wise. The matrices must have the same dimensions.
+
+$A=\begin{bmatrix}1&2\cr3&4\end{bmatrix} B=\begin{bmatrix}5&6\cr7&8\end{bmatrix}$
+
+$A + B = \begin{bmatrix}1+5 & 2+6 \\ 3+7 & 4+8\end{bmatrix} = \begin{bmatrix}6 & 8 \\ 10 & 12\end{bmatrix}$
+
+### Matrix Multiplication
+Matrix multiplication is performed by taking the dot product of the rows of the first matrix with the columns of the second matrix.
+
+$A=\begin{bmatrix}1&2\cr3&4\end{bmatrix} B=\begin{bmatrix}5&6\cr7&8\end{bmatrix}$
+
+$A \cdot B = \begin{bmatrix}1\cdot5+2\cdot7 & 1\cdot6+2\cdot8 \\ 3\cdot5+4\cdot7 & 3\cdot6+4\cdot8\end{bmatrix} = \begin{bmatrix}19 & 22 \\ 43 & 50\end{bmatrix}$
+
+### Matrix Transpose
+The transpose of a matrix $A$ is obtained by swapping the rows and columns. It is denoted by $A^T$.
+
+$A=\begin{bmatrix}1&2\cr3&4\end{bmatrix}$
+$A^T=\begin{bmatrix}1&3\cr2&4\end{bmatrix}$
+
+### Identity Matrix
+
+The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It is denoted by $I$.
+
+$I=\begin{bmatrix}1&0\cr0&1\end{bmatrix}$
+
+### Matrix Inverse
+
+The inverse of a matrix $A$ is denoted by $A^{-1}$. It is the matrix such that $A \cdot A^{-1} = I$, where $I$ is the identity matrix.
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