Packet 9: Tossup 7

A variant of this property, which adds a prefix to its name, is possessed by the input of the Thomas algorithm and the output of the Lanczos algorithm. If a matrix has this property, its Gerschgorin circles are simply points. A form of (15[1])“dominance” (-5[1])named (-5[1])for this property (-5[2])implies (-5[1])convergence (-5[1])of the Jacobi and Gauss-Seidel algorithms. A matrix with this property (15[1])is added to a nilpotent matrix in a (15[1])Jordan normal form. (15[1]-5[1])Orthogonal (15[1]-5[1])matrices (-5[1])(*) sandwich a matrix with this (10[1])property (10[1]-5[1])in the (10[1])statement (10[1])of the spectral (10[2])theorem. (10[2])A matrix (10[2])has this property (10[1])if it simultaneously (-5[1])has the properties that define (10[1])both L and U (10[1])in an (10[1])LU decomposition. (10[1]-5[1])A matrix is similar to one (10[1])with this property (-5[2])if it has a basis of eigenvectors. For 10 points, name this property of a matrix whose nonzero entries have the same row (10[1])and column. (10[1])■END■ (10[8]0[11])

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