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

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

  • An identity matrix InI_n is a matrix that does not change any vector xx when we multiply that vector by that matrix. Inx=xI_nx = x

Inverse Matrix

  • Denoted by A1A^{-1}; where A1A=InA^{-1}A = I_n

  • Use case: A1A^{-1} can be used to solve linear equations:

Ax=bStep_1:Multiply by A1A1Ax=A1bStep_2:A1A=InInx=A1bStep_3:Multiplying with In will not change the vectorx=A1bAx=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


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