Questions tagged [generalizedeigenvector]

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44 questions
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Intuition of generalized eigenvector.

I was trying to get an intuitive grasp about what the the generalized eigenvector intuitively is. I read this nice answer, so I understand that in the basis given by the generalized eigenvectors, a ...
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Exponential of a Matrix- Repeated AND Complex Eigenvalues

I am seeking a general solution to the initial value problem x' = Ax, x(0) = x_0 that can be written out to include both the eigenvalues and eigenvectors. To cover the case of repeated eigenvalues, ...
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How to use random projections to find matrices A,B s.t. AX=BY

(This is for my graduate research -- not exactly homework) Given an arbitrary $X \in \Re^{M_X \times N}, Y \in \Re^{M_Y \times N}$, I want to find $A \in \Re^{K \times M_X}, B \in \Re^{K \times M_Y}$...
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Constructing matrices with the given eigenvalue and eigenspace

There are several similar questions: (a) If possible, write down a 5 × 5 real matrix with −1 as its only real eigenvalue and where the eigenspace with eigenvalue −1 has dimension 3. (b) If possible, ...
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Generalized eigenvectors from left and right Schur vectors

I am reading up on the generalized Schur decomposition as a means to solve the generalized eigenvalue problem $A\nu = \lambda B \nu$, With $A$ and $B$ matrices, $\lambda$ the eigenvalues and $\nu$ ...
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Second-order matrix equations

Let $A\in\mathbb{R}^{n\times n}$, $B\in\mathbb{R}^{n\times p}$, $C\in\mathbb{R}^{q\times n}$ and $D\in\mathbb{R}^{q\times p}$ be known matrices. Denote by $I_n$ the identity matrix of size $n\times n$ ...
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Find a constant to bound laplacian norm by gradient norm in finite dimension

I need to prove (P). For prove that, the hint is to use (D). My question is, how to use (D) to prove (P)? Let $T$ a triangle or tetrahedron and $\mathbb{P}_k(T)$ the set of polynomials of degree less ...
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question regarding generalized eigenvectors for Differential equation

I also have a question about the generalized eigenvector, I learned how to find the generalized vector in class, but for this practice problem, I am not sure how to find the generalized eignvectors ...
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Generalized eigenvectors for Jordan canonical form (and theory)

I am learnnig how to find a Jordan normal form of a matrix, and I got stuck on four items. Can you please explain to me and check if I am right with my understanding? (I do not have a real example on ...
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Can a polynomial with degree (r+s-1) have (r+s) distinct roots?

While reading about generalised eigenvectors, i came to a strange proof. It goes like If p is a polynomial which has r distinct roots {λ1,λ2...,λr}, and q is a polynomial with s distinct roots {μ1,μ2....
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How to find generalized Eigen vectors of a matrix with Eigen vectors already on diagonal?

I have a matrix A= \begin{bmatrix} 1 & -1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1\\ 0 & 0 & 1 & 1 \end{bmatrix} This matrix has ...