Purchase Solution

Fundamental Mathematics: Eigenvectors and Matrices

Not what you're looking for?

Ask Custom Question

1) Find the eigenvectors and eigenvalues of the matrix A. Hence find the matrix P and a diagonal matrix D such that A = P^?1 DP and compute A^100 (see attached).

2.i) Verify the Cayley-Hamilton theorem for the matrix A.
ii) Compute the minimal polynomial of a matrix A and decide whether the matrix is diagonalizable or not. The same question for the matrix B (see attached).

Attachments
Purchase this Solution
Solution Summary

We solve several problems in linear algebra.

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.

Probability Quiz

Some questions on probability

Exponential Expressions

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

Solving quadratic inequalities

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

Multiplying Complex Numbers

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

View More Free Quizzes
Related BrainMass Solutions

  • Linear algebra: finding eigenvalues

    I need to find the eigenvectors of each data series. How do I derive the eigenvalues (or eigenvectors) and what are they from this data set?

  • Matrices

    Then we set , then The eigenvectors for , and are , , . Thus the fundamental matrix is , So the real fundamental matrix is The general solution is (a) If , then . So the solution is (b) If , then .

  • 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.

  • Eigenvectors and eigenvalues

    This provides examples of working with eigenvectors and eigenvalues of matrices.

  • Diagonalizability

    A real valued n by n matrix is diagonalizable if and only if there are n linearly independent eigenvectors. Any set of eigenvectors corresponding to distinct eigenvalues are automatically linearly independent.

  • Linear Algebra : Hermitian Similar Matrices

    30855 Linear Algebra : Hermitian Similar Matrices Suppose A & B are Hermitian matrices and AB=BA, show that A and B are simultaneously diagonalizable, ie, there exists an unitary matrix C so that both C*AC adn C*BC are diagonal. Hi there!

  • Matrix Theory - Isometries

    If sint=0 this means that cost is 1 or -1 and we get diagonal matrices with 1 and -1 on the diagonal; in this case the eigenvectors are of course (u,0) and (0,u), as with any diagonal matrix.

  • Eigenvalues and Dimension of Corresponding Eigenspace (4 Problems)

    50760 Eigenvalues and Dimension of Corresponding Eigenspace Determine the eigenvalues and eigenvectors of each of the following matrices. For each eigenvalue, determine the dimension of the corresponding eigenspace.

  • Fundamental Mathematics: Rotation & Reflection

    516950 Fundamental Mathematics: Rotation & Reflection in three dimensional space We use matrices, eigenvalues and eigenvectors to solve the following: Let f be the rotation in the 3-dimensional space about the x-axis through the angle pi/2 and g be

View More Related Solutions