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Matrix Algebra - Coggle Diagram
Matrix Algebra
Special Types of Matrices
Identity Matrix
Zero Matrix
Diagonal Matrix
Upper and Lower Triangular Matrices
Symmetric and Skew-Symmetric Matrices
Basics of Matrices
Definition of a Matrix
Matrix Notation
Matrix Dimensions (Rows and Columns)
Scalar, Row, Column, and Square Matrices
Matrix Operations
Addition and Subtraction of Matrices
Scalar Multiplication of a Matrix
Matrix Multiplication
Row-Column Rule
Properties of Matrix Multiplication
Transpose of a Matrix
Matrix Operations and Applications
Solving Systems of Linear Equations
Matrix Transformations
Matrix Representations of Graphs
Markov Chains and Transition Matrices
Applications of Matrix Algebra in Computer Science
Computer Graphics and Image Processing
Machine Learning and Data Analysis
Network Analysis and Graph Theory
Cryptography and Error Correction Codes
Matrix Inverse
Invertible Matrices (Non-Singular Matrices)
Finding the Inverse of a Matrix
Properties of Inverse Matrices
Matrix Determinants
Determinant of a Matrix
Properties of Determinants
Cramer's Rule for Solving Linear Equations
Eigenvalues and Eigenvectors
Characteristic Equation
Eigenvalues and Eigenvectors
Diagonalization of Matrices
Matrix Factorizations
LU Decomposition
QR Decomposition
Singular Value Decomposition (SVD)
Matrix Calculus
Gradient of a Matrix
Jacobian Matrix
Matrix Derivatives
Matrix Norms
Vector Norms
Matrix Norms
Properties of Norms
Matrix Equations
Linear Systems of Equations
Matrix Equation AX = B
Homogeneous and Non-Homogeneous Systems