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Positive Input Reachability And Controllability Of Positive Systems
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 × nExpand
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THE WEYR CHARACTERISTIC
(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
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 isExpand
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Mathematical aspects of the relative gain array ( AΦHA —T )
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
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Upper bounds on the minimum distance of trellis codes
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 dataExpand
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Simultaneous block triangularization and block diagonalization of sets of matrices
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 ofExpand
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A survey of canonical forms and invariants for unitary similarity
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. TheExpand
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Linear Algebra and Matrices: Topics for a Second Course
Preliminaries Inner product spaces and orthogonality Eigenvalues, eigenvectors, diagonalization, and triangularization The Jordan and Weyr canonical forms Unitary similarity and normal matricesExpand
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To the Latimer-Macduffee theorem and beyond!
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 anExpand
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Schur's Lemma for Coupled Reducibility and Coupled Normality
TLDR
We prove versions of Schur's Lemma for $\mathcal A, \mathcal B$ satisfying coupled irreducibility conditions. Expand
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