One of the most important theorems in Linear Algebra is Cayley-Hamilton theorem: q(T) =0. We know q(T) = 0 and deg q = n. Is it possible we find another polynomial p(t) for which p(T) = 0 and deg p <= deg q? The answer is yes. Such polynomial p is called minimal ...
Moreover, it shows that a finite dimensional Lie algebra is solvable if and only if the characteristic polynomial is completely reducible.doi:10.1016/j.laa.2018.11.015Zhiguang HuPhilip B. ZhangLinear Algebra and its ApplicationsZ. Hu, P.B. Zhang, Determinants and characteristic polynomials of ...
Numerous cryptographic protocols and scientific computations are based on linear algebra, which can be reduced to some core problems, such as matrix multiplication, determinant and the characteristic polynomial of a matrix. However, it is difficult to carry out these expensive computations independently ...
Tropical algebraMatrix theoryLetχ(A)denote the characteristic polynomial of a matrixAover a field; a standard result of linear algebra states thatχ(A−1)is the reciprocal polynomial ofχ(A). More formally, the conditionχn(A)χk(A−1)=χn−k(A)holds for any invertiblen×nmatrixA...
LinearAlgebra[Modular] IntegerCharacteristicPolynomial computation of the characteristic polynomial of an integer matrix using modular methods Calling Sequence Parameters Description Examples Calling Sequence IntegerCharacteristicPolynomial( A , lambda..
Li. Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General ... HH Zhang,WB Yan,LI Xue-Song - 《理论物理通讯(英文版)》 被引量: 0发表: 2008年 The proof complexity of linear algebra We give what is apparently the...
We derive a new algorithm for computing the reduced primary decomposition of I using only standard linear algebra and univariate polynomial factorization ... CHRIS MONICO - 《Journal of Symbolic Computation》 被引量: 64发表: 2002年 On the computation of the characteristic polynomial of a matrix In...
Linear Algebra Vectors Matrix Characteristic Polynomial Examples characteristicpolynomial( 1−4 4−7 ) characteristicpolynomial( 121 6−10 −1−2−1 ) characteristicpolynomial( a1 02a ) Description Find the Characteristic Polynomial of a matrix step-by-step ...
Since χ−z0 is a polynomial of {ψj,ψ¯j}j=1n with zero free term, there exists l∈N such that (χ−z0)l=0, and hence the series terminates after a finite number of terms. The integral over the Grassmann variables is a linear functional, defined on the basis by the ...
PDEtools CharacteristicQ compute the characteristic of a point symmetry represented by its infinitesimals Calling Sequence Parameters Description Examples Calling Sequence CharacteristicQ(S, DepVars, 'options'='value') Parameters S - a list with the...