diff --git a/nav_onboarding/README.md b/nav_onboarding/README.md new file mode 100644 index 0000000..f7cd1da --- /dev/null +++ b/nav_onboarding/README.md @@ -0,0 +1,49 @@ +## 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. + + + + + + + + + + + +