# Machine Learning - Linear Algebra

Linear Algebra review
Fundation of machine leaning(Matrices and vectors)

## Matrix

• Rectangular array of numbers
• Dimension of matrix number of rows x number of columns

## Vector

• An n x 1 matrix

## Scalar multiplication

• Multiplication: scalar number multiply matrix will take every elements to multiple result in matrix, the result is same as dimension matrix

## Matrix-vector multiplication

• m x n matrix multiply n dimention vector turns out m demention vector. • m x n matrix multiply n x o matrix turns out m x o matrix.

## Matrix Multiplication Properties

• Let A and B be matrices. Then in general, A X B ≠ B X A.(not commutative)

• A X B X C. Let D = B X C, then A X D, equals E = A X B, then E X C.(associative)

• Identity Matrix, Denoted I ( or Inxn). For any matrix A, A X I = I X A = A, but the I is not same maybe.

## Inverse and transpose

• Not all numbers have an inverse.

• If A is an m x m matrix(square matrix), and if it has an inverse, A A-1 = A-1 A = I.

• Matrices that don’t have an inverse are “singular” or “degenerate”

• Matrix transpose. A and AT

• Let A be an m x n matrix, and let B = AT. Then B is an n x m matrix, and Bij = Aji