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Reductions and transformations
jfylVIethods for the dominant eigenvalue
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analysis annihilate applied approximation As+i Chapter choose coefficients column complete eigensystem computed consider corresponding eigenvectors decomposition defined deflation processes denote determine diagonal elements diagonal form diagonal matrix dominant eigenvalue eigen eigensystem eigenvalue problem eigenvectors xi elementary divisors elementary Hermitian matrices elementary unitary matrices equation evaluate example exercise find the eigenvalues follows given gives Hermitian matrix Hk+i Householder's method introduced inverse iteration Jacobi method Laguerre's method linear LU decomposition matrix H modulus non-singular non-zero normal obtained off-diagonal elements orthogonal pivot plane rotations polynomial positive definite postmultiplication power method premultiplication procedure QR algorithm QR process Rayleigh quotient real symmetric reduce result Section 3.4 sequence of matrices Show similarity transformation solution step Sturm sequence Sturm sequence property subdiagonal elements symmetric matrix symmetric tridiagonal matrix technique Theorem tion tridiagonal form tridiagonal matrix unitary matrix upper Hessenberg form upper Hessenberg matrix upper triangular matrix values vector zero