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Matrix Operations - Overview

Introduction​

High-level overview of matrix multiplication, LU decomposition, and special matrices.

Key Concepts​

Matrix Multiplication​

  • Row-column interpretation
  • Column interpretation
  • Row interpretation
  • Block multiplication

LU Decomposition​

  • Triangular factors
  • When LU exists
  • Permutation matrices (PLU)

Special Matrices​

  • Symmetric matrices
  • Orthogonal matrices
  • Diagonal matrices
  • Identity and zero matrices
  • Triangular matrices

Applications​

  • Solving linear systems efficiently
  • Matrix factorizations in ML
  • Numerical stability

References​