منابع مشابه
The Jordan Canonical Form
Let β1, . . . , βn be linearly independent vectors in a vector space. For all j with 0 ≤ j ≤ n and all vectors α1, . . . , αk, if β1, . . . , βn are in the span of β1, . . . , βj, α1, . . . , αk, then j + k ≥ n. The proof of the claim is by induction on k. For k = 0, the claim is obvious since β1, . . . , βn are linearly independent. Suppose the claim is true for k−1, and suppose that β1, . . ....
متن کاملThe Jordan canonical form
4 The minimal polynomial of a linear transformation 7 4.1 Existence of the minimal polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 The minimal polynomial for algebraically closed fields . . . . . . . . . . . . . . . . . 8 4.3 The characteristic polynomial and the Cayley–Hamilton theorem . . . . . . . . . . . 9 4.4 Finding the minimal polynomial . . . . . . . . . . . . . ....
متن کاملJordan Canonical Form
is the geometric multiplicity of λk which is also the number of Jordan blocks corresponding to λk . • The orders of the Jordan Blocks of λk must sum to the algebraic multiplicity of λk . • The number of Jordan blocks corresponding to an eigenvalue λk is its geometric multiplicity. • The matrix A is diagonalizable if and only if, for any eigenvalue λ of A , its geometric and algebraic multiplici...
متن کاملEnhancing the Jordan canonical form
The Jordan canonical form parametrises similarity classes in the nilpotent cone Nn, consisting of n× n nilpotent complex matrices, by partitions of n. Achar and Henderson (2008) extended this and other well-known results about Nn to the case of the enhanced nilpotent cone C ×Nn. 1. Jordan canonical form The Jordan canonical form (JCF), introduced in 1870 [10], is one of the most useful tools in...
متن کاملComputational Aspects of the Jordan Canonical Form
In this paper we discuss algorithmic aspects of the computation of the Jordan canonical form. Inspired by the Golub & Wilkinson paper 9] on the computation of the Jordan canonical form, an O(n 3) algorithm was developed by Beelen & Van Dooren 3] for computing the Kronecker structure of an arbitrary pencil B ? A. Here we show how the ideas of this algorithm lead to a special algorithm for recons...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.12.030