Linear Algebra: Deep Learning Book

Linear algebra is a form of continuous rather than discrete mathematics.

Scalars, Vectors, Matrices and Tensors

Multiplying Matrix and Vectors

Identity and Inverse Matrix

Identity Matrix

• $I_n \in \mathbb{R}^{n \times n}$; where main diagonal = 1's and all other entries = 0's

• An identity matrix $I_n$ is a matrix that does not change any vector $x$ when we multiply that vector by that matrix. $I_nx = x$

Inverse Matrix

• Denoted by $A^{-1}$; where $A^{-1}A = I_n$

• Use case: $A^{-1}$ can be used to solve linear equations:

$$Ax=b \newline Step \_1: Multiply \ by \ A^{-1} \newline A^{-1}Ax=A^{-1}b \newline Step \_2: A^{-1}A = I_n \newline I_nx = A^{-1}b \newline Step \_3: Multiplying\ with \ I_n \ will \ not \ change \ the \ vector \newline x = A^{-1}b$$

Linear dependence and Span

Link: http://www.deeplearningbook.org/contents/linear_algebra.html