Direct computation of canonical forms for linear systems by elementary matrix operations

1974 ◽  
Vol 19 (2) ◽  
pp. 124-126 ◽  
Author(s):  
J. Aplevich
Keyword(s):  
Linear Systems ◽  
Canonical Forms ◽  
Direct Computation ◽  
Elementary Matrix ◽  
Matrix Operations

scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

scholarly journals Canonical forms for linear systems

1983 ◽  
Vol 50 ◽  
pp. 437-473 ◽  
Author(s):  
D. Prätzel-Wolters
Keyword(s):  
Linear Systems ◽  
Canonical Forms

scholarly journals Direct Computation of Operational Matrices for Polynomial Bases

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Osvaldo Guimarães ◽  
José Roberto C. Piqueira ◽  
Marcio Lobo Netto
Keyword(s):  
Hilbert Space ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Operational Matrices ◽  
Direct Computation ◽  
Linear Operation ◽  
Matrix Operations ◽  
Polynomial Bases ◽  
Reference Matrix

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

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