In this section, we introduce two important polynomials of an operator: characteristic polynomial and minimal polynomials. Given T in L(V), if V is complex, then T has at least one eigenvalue. Let \…
Twitter Google Share on Facebook minimal polynomial [′min·ə·məl ‚päl·ə′nō·mē·əl] (mathematics) The polynomial of least degree which both divides the characteristic polynomial of a matrix and has the same roots.
Let $k$ be a field of characteristic two. We prove that a non constant monic polynomial $f\\in k[X]$ of degree $n$ is the minimal/characteristic polynomial of a symmetric matrix with entries in $k$ if and only if it is not the product of pairwise distinct inseparable irreducible ...
Remember that the characteristic polynomial of a matrix is where is the identity matrix. Also remember that, by the fundamental theorem of algebra, any polynomial of degree can be factorized aswhere are roots of and is a constant. The factorization is unique up to a permutation of the factors...
The least polynomial, determinant, Smith canonical form of AA(1) are also given . 给出了广义逆A+的一种计算方法及AA(1)的最小多项式、行列式、Smith标准形等。 3. The Jordan canonical form, characteristic value, characteristic vector, and the least polynomial of the generalized Drazin inverse mat...
LinearAlgebra MinimalPolynomial construct the minimal polynomial of a Matrix Calling Sequence Parameters Description Examples Calling Sequence MinimalPolynomial( A , lambda ) Parameters A - Matrix lambda - name; used as a variable Description The Minimal
We investigate the complexity of (1) computing the characteristic polynomial, the minimal polynomial, and all the invariant factors of an integer matrix, and of (2) verifying them, when the coefficients are given as input. It is known that each coefficient of the characteristic polynomial of a...
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The sequence generated by σ-LFSR is called the σ-linear recurrence sequence and its characteristic polynomial is the matrix polynomial over finite field. With analysis of the algebra structure of the matrix polynomial ring over finite field, the sufficient and necessary condition for the minimal ...
1)minimal polynomial最小多项式 1.Solving process ofminimal polynomialof the matrix equation;矩阵方程的最小多项式解法 2.In order to obtain a polynomial of less degree,the structure of Drazin inverse of matrix is analysed by using the theory of Jordan canonical matrix,and a computational method for...