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Matrices.md

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+#Math #Algebra
+
+A matrix is an $n$ by $m$ set of values. A $4 \times 3$can be notated by:
+
+$$
+\begin{bmatrix}a_1 & a_2 & a_3 \cr b_1 & b_2 & b_3 \cr c_1 & c_2 & c_3 \cr d_1 & d_2 & d_3 \end{bmatrix}
+$$
+
+To get a value from matrix $a$ in row $r$ and column $c$, use:
+
+$$
+a_{r, c}
+$$
+
+# Addition
+
+With two matrices of the same order, add corresponding elements:
+
+$$
+\begin{bmatrix} a_1 & b_1 \cr c_1 & d_1 \end{bmatrix} + \begin{bmatrix} a_2 & b_2 \cr c_2 & d_2 \end{bmatrix} = \begin{bmatrix} a_1 + a_2 & b_1 + b_2 \cr c_1 + c_2 & d_1 + d_2 \end{bmatrix}
+$$
+
+# Subtraction
+
+With two matrices of the same order, subtract corresponding elements:
+
+$$
+\begin{bmatrix} a_1 & b_1 \cr c_1 & d_1 \end{bmatrix} - \begin{bmatrix} a_2 & b_2 \cr c_2 & d_2 \end{bmatrix} = \begin{bmatrix} a_1 - a_2 & b_1 - b_2 \cr c_1 - c_2 & d_1 - d_2 \end{bmatrix}
+$$
+
+# Scalar Multiplication
+
+When multiplying a matrix by a scalar, multiply each element by said scalar:
+
+$$
+s\begin{bmatrix} a & b \cr c & d \end{bmatrix} = \begin{bmatrix} sa & sb \cr sc & sd \end{bmatrix}
+$$
+
+# Matrix Multiplication
+
+Let $a$ be an $i$ by $j$ matrix and $b$ be a $m$ by $n$ matrix. If $j = m$, $ab$ is defined.
+
+$$
+ab_{c, d} = \sum _{k = 1}^{j} a_{c, k}b_{k, d}
+$$