Toppers Notes on Matrices

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Table of Content

  • Definition.
  • Order of matrices.
  • Equality of matrices.
  • Types of matrices.
  • Elementary transfrormations.
  • Elementary operations.
  • Trace of a matrix.
  • Multiplication of matrices.
  • Properties of matrix multiplication.
  • Positive integer powers of matrices.
  • Transpose of a matrix.
  • Properties of the transpose.
  • Symmetric matrix.
  • Skew-symmetric matrix.
  • Properties of symmetric and skew-symmetric matrices.
  • Singular and non-singular matrix.
  • Hermitian and skew-hermitian matrix.
  • Orthogonal matrix.
  • Idempotent matrix.
  • Involutory matrix.
  • Nilpotent matrix.
  • Unitary matrix.
  • Periodic matrix.
  • Differentiation of a matrix.
  • Conjugate of a matrix.
  • Properties of the conjugate.
  • Transpose conjugate of a matrix.
  • Properties of transpose conjugate.
  • Adjoint of a square matrix.
  • Properties of adjoint.
  • The inverse of a matrix.
  • Properties of the inverse of a matrix.
  • Minor of a matrix.
  • The rank of a matrix.
  • The solution of the non-homogeneous system of linear equations.
  • The solution of the homogeneous system of linear equations.
  • Caley-hamilton theorem.