Multiplication

A mathematical operation

Matrix Multiplication

The art of multiplying matrices by matrices, vectors and numbers. Matrix multiplication is non-commutative as it essentially is the same as nesting mathematical functions.

The Identity Transformation

The equivalent of multiplying something by one when dealing with matrices and vectors is the identity transformation. The matrix itself looks like this (in $R^2$):

$$ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

It can also be represented functionally this way: $Id_{R^n}(x) = x, \forall x \in R^n$

Complex numbers

$z_i = a + ib, z_2 = c + id$

$z_1 + z_2 = (a + c) + i(b + d)$

$z_1 * z_2 = (ac - bd) + i(ad + bc)$