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Symmetric and skew-symmetric matrices

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  • exposé
  • cours - matière potentielle : on mechanics
21 Symmetric and skew-symmetric matrices 21.1 Decomposition of a square matrix into symmetric and skew- symmetric matrices Let Cn×n be a square matrix. We can write C = (1/2)(C + Ct) + (1/2)(C − Ct) = A+B, where At = A is symmetric and Bt = −B is skew-symmetric. Examples: • Let C =   1 2 3 4 5 6 7 8 9   .
  • infinitessimal rotation
  • facts about complex numbers
  • direction of ψ as the axis of rotation
  • taylor series expansion of the indicated thing
  • corresponding eigenvectors
  • eigenvector
  • symmetric matrix
  • complex conjugate
  • expansion
  • left hand-side
  • left hand side

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