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https://en.wikipedia.org/wiki/Canonical_form
In this context, a canonical form is a representation such that every object has a unique representation (with canonicalization being the process through which a representation is put into its canonical form). Thus, the equality of two objects can easily be tested by testing the equality of their canonical forms.
http://buzzard.ups.edu/courses/2014spring/420projects/math420-UPS-spring-2014-toomey-rational-canonical-form.pdf
the minimal polynomial. As we will later see, minimal polynomials play an important roll in nding the Rational Canonical Form of a matrix. De nition. The minimal polynomial of a matrix A, denoted m A(x), is the unique monic polynomial of least degree such that m A(A) = 0. Let us examine this notion in the context of an F[x]-module. Let V be a ...
https://everything2.com/title/Canonical+representation+of+polynomials
In dense representation, this is (x,4,1,-1,3,7,-5). In sparse representation, this is the considerably less elegant (x,4,1,3,-1,2,3,1,7,0,-5) Nonetheless, this analysis rests on the polynomial being completely dense- and this is rarely the case. Hence the convention for CA systems is …
https://www.sciencedirect.com/science/article/pii/S0021999116302303
6. Canonical low-rank approximations versus sparse polynomial chaos expansions. We next confront canonical LRA to sparse PCE in the same meta-modeling applications considered in Section 5. The focus of the comparison is set on the applications involving finite-element models.Cited by: 52
http://www.eolss.net/Sample-Chapters/C18/E6-43-13-02.pdf
©Encyclopedia of Life Support Systems (EOLSS) CANONICAL FORMS FOR STATE–SPACE DESCRIPTIONS ... models and with the representation of this structure in terms of special descriptions ... are provided by those of the echelon type canonical form of polynomial matrices.
https://www.sciencedirect.com/science/article/pii/S0377042714005123
The aim of this paper is to give a canonical representation for the elements in the ring of the continuous piecewise polynomial functions. While general piecewise polynomial functions are interesting in general, most applications of them to CAGD require the functions to be continuous.Author: Jorge Caravantes, M. Angeles Gomez-Molleda, Laureano Gonzalez-Vega
https://works.bepress.com/saeid_abbasbandy/22/download/
Canonical representation for approximating solution of fuzzy polynomial equations M. Salehnegad1, S. Abbasbandy2, M. Mosleh1, M. Otadi1* 1 Department of Mathematics, Islamic Azad University, Firuozkooh branch, Firuozkooh, IRAN 2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran Abstract
https://www.mathworks.com/help/control/ref/canon.html
If type is unspecified, then canon converts the specified dynamic system model to modal canonical form by default. The companion canonical form is the same as the observable canonical form. For information on controllable and observable canonical forms, see Canonical State-Space Realizations.
https://en.wikipedia.org/wiki/Rational_canonical_form
Where the minimal polynomial is identical to the characteristic polynomial, the Frobenius normal form is the companion matrix of the characteristic polynomial. As the rational canonical form is uniquely determined by the unique invariant factors associated to A, and these invariant factors are independent of basis, it follows that two square ...
https://math.stackexchange.com/questions/847940/polynomial-representation-of-binary
But if I use polynomial representation to compute, I obtain $(x+1)(x+1)=x^2+1$, which is $101$ in binary. Clearly it is not $9$ in decimal. Can anyone explain to me where I got wrong.
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