GateXAIML · Matrices & Linear Algebra Concept Notes

Matrices & Linear Algebra

Chapter 1
Matrices and Determinants
30 sections
Introduction, Types of Matrices, Matrix Operations...
Chapter 2
Rank and Nullity
11 sections
Vectors from Matrices, Row Space, Column Space, and Null Space, Rank of a Matrix...
Chapter 3
Eigenvalues and Eigenvectors
5 sections
Characteristic Polynomial, Finding Eigenvalues and Eigenvectors, Properties of Eigenvalues and Eigenvectors...
Chapter 4
Systems of Linear Equations
8 sections
Matrix Representation of Linear Systems, Homogeneous and Non-Homogeneous Systems, Consistency of Systems...
Chapter 5
Matrix Factorizations
2 sections
LU Decomposition, Applications of LU Factorization
Chapter 6
Special Matrices
8 sections
Projection Matrices, Orthogonal Matrices, Orthogonal...
Chapter 7
Summary - Very Important
13 sections
1. Types of Linear Systems, 2. Rank and Nullity, 3. Rouché–Capelli Theorem (Consistency)...