Matrices

Dimension of matrix = number of rows x number of columns (4x3)
Addition of two matrices of the same dimension - element wise (same for subtraction)
"Scalar Multiplication" - Multiplication of a matrix by a scalar (multiply each element by the scalar) (also scalar division)
R(3,2) x R(2) = R(3) multiply a matrix of 3 rows and 2 columns by a vector of 2 element (2 rows) (element-wise mnultiple and then sum the results)
3x2 matrix multiply by a 2x1 matrix the result is 3x1 matrix
R(m, n) x R(n) = R(m)

| 1  3 |   | 1 |   | 16 |
| 4  0 | x | 5 | = |  4 |
| 2  1 |           |  7 |

| 1 3 2 |    | 1 3 |   | 11 10 |
| 4 0 1 | x  | 0 1 | = |  9 14 |
             | 5 2 |

Matrix multiplication is not commutative, that is A x B is not the same as B x A.
Matrix multiplication is associative, that is (A x B) x C is the same as A x (B x C)
Identity Matrix I or I(nxn) is a square matrix in which everything is 0 except the diagonal that is filled with the number 1.
A x I = I x A = A
Matrix Inverse A x A(to the power of -1) = I - Only square matrices have inverse, but not all square matrices have inverse. (e.g. the all 0s matrix does not have one)
The matricses that don't have an invers are somehow close to the all 0 matrix. They are also called "singular" or "degenerate" matrices.
Matrix Transpose - (1st row becomes the 1st column; 2nd row becomes 2nd column, etc....)

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