rank and minimal polynomial
Hint If Jm1(λ1)⊕⋯⊕Jmk(λk). is the direct sum decomposition of the matrix A (already in Jordan normal form) into Jordan blocks Jmi(λi) ...,由 M Fiedler 著作 · 1981 · 被引用 3 次 — The following theorem is proved: If r is the degree of the minimal polynomial of a matrix A then there exists a principal submatrix of A with order r and rank ...
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 rank and minimal polynomial 相關參考資料
(mathbbR})$ with $nge 2$ has rank $1$ - Mathematics Stack ...
In this case, A is diagonalizable with minimal polynomial p(x)=x(x−λ) for non-zero eigenvalue λ. The other possibility is that 0 is the only eigenvalue of A. https://math.stackexchange.com Classifying the minimal polynomials of n×n matrices of rank 2
Hint If Jm1(λ1)⊕⋯⊕Jmk(λk). is the direct sum decomposition of the matrix A (already in Jordan normal form) into Jordan blocks Jmi(λi) ... https://math.stackexchange.com Minimal polynomial and the rank of principal submatrices of a ...
由 M Fiedler 著作 · 1981 · 被引用 3 次 — The following theorem is proved: If r is the degree of the minimal polynomial of a matrix A then there exists a principal submatrix of A with order r and rank ... https://www.tandfonline.com Minimal polynomial of matrix with rank 1 - Mathematics Stack ...
There is a general proposition about full rank decomposition: If A is an m×n matrix of rank r, then there exists full column rank(=r) matrix ... https://math.stackexchange.com Minimum and Characteristic Polynomials of Low-Rank Matrices
由 WP Wardlaw 著作 · 1995 · 被引用 2 次 — determination of the minimum polynomial or the null ideal of A. ... of rank r is annihilated by a certain polynomial of degree r + 1; this polynomial turns. http://www.jstor.org Rank of a linear operator given its characteristic and minimal ...
Let T:V→V be a linear operator on the vector space V with characteristic polynomial λ4(λ−4)5 and minimal polynomial λ(λ−4), then what is the rank of T? https://math.stackexchange.com What does the degree of a matrix minimal polynomial encode ...
If A has distinct n non-zero eigen values in an extension field of F, μ is the characteristic polynomial of A. Hence deg μ=n= rank A. https://math.stackexchange.com What is rank of $f(A)$, where $f$ is the minimal polynomial of ...
From the definition of minimal polynomial f(A)=0. Hence f(A) is the zero transformation. Hence rank is 0. https://math.stackexchange.com |