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Positive Input Reachability And Controllability Of Positive Systems

- P. Coxson, H. Shapiro
- Mathematics
- 1 September 1987

Abstract We study controllability and reachability for discrete linear control systems, x ( k + 1) = Ax ( k ) + Bu ( k ), in which the state vector x ( k ), the control vector u ( k ), the n × n… Expand

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THE WEYR CHARACTERISTIC

- H. Shapiro
- Mathematics
- 1 December 1999

(1999). The Weyr Characteristic. The American Mathematical Monthly: Vol. 106, No. 10, pp. 919-929.

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Pairs Of Matrices With Quadratic Minimal Polynomials

- F. Gaines, T. Laffey, H. Shapiro
- Mathematics
- 1 July 1983

Abstract Let A, B be n × n matrices over a field F, and suppose A, B have quadratic minimal polynomials. Then the algebra generated by A, B has dimension at most 2n − 1 if n is odd and 2n if n is… Expand

15 2

Mathematical aspects of the relative gain array ( AΦHA —T )

- C. Johnson, H. Shapiro
- Mathematics
- 1 October 1986

For nonsingular n-by-n matrices A, we investigate the map \[ A \to \Phi ( A ) \equiv A \circ ( A^{ - 1} )^T \] in which $ \circ $ denotes the Hadamard (entry-wise) product. The matrix $\Phi ( A )$… Expand

35 1

Upper bounds on the minimum distance of trellis codes

- A. Calderbank, J. Mazo, H. Shapiro
- Mathematics
- 1 October 1983

A trellis code is a “sliding window” method of encoding a binary data stream into a sequence of real numbers that are input to a noisy transmission channel. When a trellis code is used to encode data… Expand

12

Simultaneous block triangularization and block diagonalization of sets of matrices

- H. Shapiro
- Mathematics
- 1 June 1979

Abstract We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of… Expand

26

A survey of canonical forms and invariants for unitary similarity

- H. Shapiro
- Mathematics
- 1 March 1991

Abstract Matrices A and B are said to be unitarily similar if U ∗ AU = B for some unitary matrix U. This expository paper surveys results on canonical forms and invariants for unitary similarity. The… Expand

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Linear Algebra and Matrices: Topics for a Second Course

- H. Shapiro
- Mathematics
- 8 July 2015

Preliminaries Inner product spaces and orthogonality Eigenvalues, eigenvectors, diagonalization, and triangularization The Jordan and Weyr canonical forms Unitary similarity and normal matrices… Expand

5

To the Latimer-Macduffee theorem and beyond!

- H. Shapiro
- 2003

In this paper we discuss some of the mathematical contributions made by Olga Taussky Todd. We begin with fairly general considerations, commenting on her role as a thesis advisor and giving an… Expand

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Schur's Lemma for Coupled Reducibility and Coupled Normality

- D. Lahat, C. Jutten, H. Shapiro
- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 20 November 2018

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