matrices

Content

• Italic: Definition
• Bold: Theorem/Corollary

Basic matrix operations

• Matrix
• Matrix Equality
• Matrix Operations
• Matrix Scalar Multiplication
• Matrix Product
• Properties of Matrix Arithmetic
• Powers of a Matrix
  • Properties of Negative Exponents of Matrix

Matrix forms

• Zero Matrix
  • Properties of Zero Matrix
• Identity Matrix
  • Properties of Inverse Matrix
• Diagonal Matrix
• Triangular Matrix
  • Properties of Triangular Matrix
• Symmetric Matrix
  • Algebraic Properties of Symmetric Matrix
  • Commutativity Condition for Symmetric Matrix Products
  • Inverse of Symmetric Matrices are Symmetric
  • Product of a Matrix with its Transpose is Symmetric
• Idempotent Matrix
• Orthogonal Matrix
• Definite Matrix
• Partitioned Matrices and Submatrix
  • Principal Submatrix
  • TODO Scalar Multiples, Transposes, Sums, and Products of Partitioned Matrices
  • Determinants of Partitioned Matrices
  • Inverse of Partitioned Matrices
• Augmented Matrix

Matrix transformations and operations

• Trace of a Matrix
• Transpose Matrix
  • Properties of Transpose Matrix
  • Transpose of Invertible Matrix
• Inverse Matrix
  • Matrix Invertibility
  • Inverse of Matrix Product
• Generalized Inverse Matrix
• Row Echelon Form (REF)
  • Reduced Row Echelon Form (RREF)
    • Gaussian Elimination
    • Gauss-Jordan Elimination
    • Form of RREF
• Kronecker Product
• Vec Function
• Vech Function
• Matrix Transformation
• Kernel
• Range

Eigenvalues and eigenvectors

• Eigenvalue
• Eigenvector
• Similar Matrices

Matrix decomposition

• Gram-Schmidt Orthogonalization
  • QR Decomposition
• Singular Value Decomposition

Matrix calculus

• Vector Function
• Gradient Operator
• Jacobian Matrix
• Hessian Matrix
• Matrix Differentiation Properties
• Matrix Integration

Linear spaces

• Linear Space

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