Round 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 “dominance” named for this property implies convergence (-5[1])of the Jacobi and Gauss-Seidel algorithms. A matrix with this property is added to a nilpotent matrix in a (15[1])Jordan normal form. (-5[1])Orthogonal matrices (*) sandwich a matrix with this property in the statement of the spectral theorem. A matrix has this property (10[1])if it simultaneously has the properties that define both L and U in an LU decomposition. A matrix is similar to one with this property if it has a basis of eigenvectors. For 10 points, name this property of a matrix whose nonzero entries have the same row and column. ■END■ (10[1]0[1])

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