3. Linear Algebra review (optional)

3.1 Matrices and vectors

An vector is a matrix that has only 1 column, so you have an nx1 matrix

$y^i=i^{th}$ element

Math: 1-indexed vectors

Machine learning: 0-indexed vectors

(By convention, most people will use upper case to refer to matrices and usually we’ll use lower case to refer to either numbers, or just raw numbers or scalars or to vectors.)

3.2 Addition and scalar multiplication

scalar refers to a number or a real number

3.3 Matrix-vector multiplication

3.4 Matrix-matrix multiplication

3.5 Matrix multiplication properities

1. not commutative
2. is associative
3. identity matrix

3.6 Inverse and transpose

Use open source to compute inverses of matrices.

Matrices that don’t have an inverse are “sigular” or “degenerate”.

4. Linear Regression with multiple variables

4.1 Multiple features

4.2 Gradient descent for multiple variables