- Linear Algebra review
- Fundation of machine leaning(Matrices and vectors)
- Rectangular array of numbers
- Dimension of matrix number of rows x number of columns
- An n x 1 matrix
- Matrix Addition: you can only add two same dimension matrix
- Multiplication: scalar number multiply matrix will take every elements to multiple result in matrix, the result is same as dimension matrix
- 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