Matrices - Symmetric and Skew-Symmetric Matrix

  • A symmetric matrix is a square matrix in which the elements above the main diagonal are equal to the elements below the main diagonal.
  • All the main diagonal elements of a symmetric matrix are also equal.
  • Example of a symmetric matrix: [ 1 4 7 ] [ 4 2 -5 ] [ 7 -5 3 ]
  • A skew-symmetric matrix is a square matrix in which the elements above the main diagonal are equal to the negation of the elements below the main diagonal.
  • The main diagonal elements of a skew-symmetric matrix are always zero.
  • Example of a skew-symmetric matrix: [ 0 2 -9 ] [ -2 0 -7 ] [ 9 7 0 ]
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Matrices - Symmetric and Skew-Symmetric Matrix A symmetric matrix is a square matrix in which the elements above the main diagonal are equal to the elements below the main diagonal. All the main diagonal elements of a symmetric matrix are also equal. Example of a symmetric matrix: [ 1 4 7 ] [ 4 2 -5 ] [ 7 -5 3 ] A skew-symmetric matrix is a square matrix in which the elements above the main diagonal are equal to the negation of the elements below the main diagonal. The main diagonal elements of a skew-symmetric matrix are always zero. Example of a skew-symmetric matrix: [ 0 2 -9 ] [ -2 0 -7 ] [ 9 7 0 ]