Purchase Solution

Matrix and eigenvalues

Not what you're looking for?

Ask Custom Question

Please see the attached Word document.
Thank-you for your help.

3.
Suppose that A is a square matrix, and that the only eigenvectors of A are scalar multiples of the vector:

Deduce as much information as you can about A, by answering the following questions. Give reasons for your answers.

(a) What size is A?

(b) How many eigenvalues does A have? Can you tell what the eigenvalues are?

(c) What can you tell about the algebraic and geometric multiplicities?

(d) Can you tell whether or not A is diagonalizable?

Attachments
Purchase this Solution
Solution Summary

This provides examples of working with a matrix regarding eigenvalues, diagonalizability, and multiplicities.

Solution Preview

Hello

Please find the solution in the attached file.

3.
Suppose that A is a square matrix, and that the only eigenvectors of A are scalar multiples of the vector:

Deduce as much information as you can ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Matrices Eigenvalues, eigenspace, and eigenbasis.

    446911 Matrices Eigenvalues, eigenspace, and eigenbasis. Matrices Eigenvalues, eigenspace, and eigenbasis. See attached file. For each of the matrices, find all (real) eigenvalues.

  • Rotation matrices

    201494 Eigenvalues, eigenvectors, and other properties of given matrix Consider the matrix A = (cos t sin t) (-sin t cos t) Show that it is unitary Show that the eigenvalues are exp(it) and exp(-it) find the eigenvectors Verify that

  • Idempotent and nilpotent matrix proofs

    Problem #5 Since is a matrix with characteristic polynomial . So has eigenvalues 1 and 3. We can find a non-singular matrix , such that , where . Then . So we have Therefore, .

  • Finding Eigenvalues Matrix Index

    So, we know that the eigenvalues of are and Note. has n-1 eigenvalues which are equal to . The determinant and eigenvalues of a matrix index is analyzed.

  • Solving for Eigenvalues

    15516 Solving for Eigenvalues A certain 4x4 real matrix is known to have these properties: 1) Two of the eigenvalues of A are L1= 3 and L2= 2. 2) The number 3 is an eigenvalue of the matrix A + 2I. 3) det. A = 12.

  • eigenvalues and eigenvectors of matrix

    Find the eigenvalues and eigenvectors for the projection matrix P = [0.2 0.4 0; 0.4 0.8 0; 0 0 1]; 2. Find the eigenvalues for the permutation matrix P = [0 1 0; 0 0 1; 1 0 0]; 3.

  • Eigenvalues of Matrix

    30664 Eigenvalues of Matrix Calculate the eigenvalues of this matrix: {see attachment} Note: You'll probably want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues.

  • Diagonalizability

    A= The eigenvalues are . Since the eigenvalues are distinct, the eigenvectors will be linearly independent and so the matrix is diagonalizable (in fact, any symmetric matrix is diagonalizable).

  • eigenvalue

    (a) Prove that if A and B are both invertible n x n matrices, then AB and BA have the same eigenvalues.

  • Eigenvalues and Generalized Eigenvectors of a Matrix

    The eigenvector matrix is given as: S = Now eAt = SΛtS-1 = Eigenvalues and generalized eigenvectors of a matrix are found.

View More Related Solutions