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Boron canonical form P'AP Cayley-Hamilton theorem cloth bound Dfl column row defined definite hermitian matrix definite real symmetric determinant diagonal elements diagonal matrix edited by J. R. M. eigen eigenvalues and eigenvectors equivalent transformation factorisation Find all matrices Find the eigenvalues hence hermitian congruent transformation hermitian conjugate Hint idempotent inverse J. R. M. Radok Leo F linear forms linear relation linearly independent lower triangular matrix mathematics matrix of order matrix theory non-singular matrix non-singular upper triangular non-singular w-square matrix non-zero elements normal matrix normalised eigenvectors oO J oO order mxn P'AP is called polynomial positive definite hermitian positive definite real positive integer prove real orthogonal matrix real orthogonal transformation real symmetric matrix row column Russian edition satisfies the relation scalar matrix similarity transformation singular matrix skew-hermitian skew-hermitian matrix skew-symmetric matrix Special Matrices square tion by Leo transformation which reduces Translated unitary transformation upper triangular matrix vectors Verify Xx implies