Symmetric and skew-symmetric matrices

• 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