Mathematical Foundations for Machine Learning

Define vectors and matrices and perform fundamental operations: addition, scalar multiplication, and transposition.

Compute the dot product of two vectors and the product of two matrices, and interpret their meaning.

Calculate the determinant and inverse of a square matrix and relate them to the concept of invertibility.

Explain the geometric interpretation of a matrix as a linear transformation.

Define eigenvalues and eigenvectors and describe their geometric significance.

Perform eigendecomposition on a matrix to diagonalize it.

Implement vector and matrix operations from scratch in Python.

Perform fundamental linear algebra operations (e.g., matrix multiplication, inversion, eigendecomposition) using NumPy.