Matrix Inequalities for Iterative Systems

Nonfiction, Science & Nature, Mathematics, Combinatorics, Algebra
Cover of the book Matrix Inequalities for Iterative Systems by Hanjo Taubig, CRC Press
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Author: Hanjo Taubig ISBN: 9781351679091
Publisher: CRC Press Publication: February 3, 2017
Imprint: CRC Press Language: English
Author: Hanjo Taubig
ISBN: 9781351679091
Publisher: CRC Press
Publication: February 3, 2017
Imprint: CRC Press
Language: English

The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

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The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

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