Linear Algebra

Matrix Basics

1. Introduction to Matrices

2. Types of Matrices

3. Matrix Operations

4. Transpose of Matrix

5. Determinant of Matrix

6. Adjoint and Inverse of a Matrix

   1. adj A = the transpose of the matrix of co-factors 

   2. The product of a matrix A and its adjoint is equal to the unit (identity) matrix multiplied by the determinant A. Let A be a square matrix, then (Adjoint A). A = A. (Adjoint A) = | A |. I 

   3. If A and B are two square matrices of the same order, such that AB = BA = I (I = unit matrix), then B is called the inverse of A, i.e., B = A–1, and A is the inverse of B. 

   4. Inverse of a matrix by using the adjoint matrix. A–1 = (adj A) /  | A |  

7. Rank of a Matrix and Special Matrices

8. Solving Linear Equations Using Matrix

9. Eigen Values & Vector-1 

10. Eigen Values & Vector-2 

11. Eigen Values & Vector - Intuition 

12. Singular Value Decomposition (SVD)

13. Principal Component Analysis (PCA)

14. SVD & PCA

Tensors

15. Tensor Basics