Purchase Solution

The characteristic polynomial of a matrix and its inverse

Not what you're looking for?

Ask Custom Question

Linear Algebra
Matrices
Eigen Values and Eigen Vectors(II)

If A = [1, -2 , 3; 2 , 3 , -1; -3 , 1 , 2] , then find the characteristic polynomial for the matrix.
Show how this can be used to find A^(-1).

The fully formatted problem is in the attached file.

Attachments
Purchase this Solution
Solution Summary

It is an explanation for finding the Characteristic polynomial of a matrix and inverse of a matrix. It also explains for applying the Cayley Hamilton Theorem. The solution is given in detail.

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

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

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Solving for Eigenvalues

    So we have We get the characteristic polynomial of is Note: If A has an inverse matrix and has an non-zero eigenvalue a, then 1/a is an eigenvalue of its inverse matrix. You can prove it easily.

  • characteristic polynomial

    Please refer to the attached file for the proper formatting. Recall that the characteristic polynomial of a linear operator T is det(A - xI) where A is the matrix of T, and I is the identity matrix. Suppose that B is the matrix of U.

  • Eigenvectors and eigenvalues

    This shows how to compute the characteristic polynomial and all eigenvalues and all eigenvectors, and show that given values are the eigenvalues of an inverse transformation matrix.

  • Matrices, Eigenvectors, Eigenvalues and Inverses

    100326 Matrices, Eigenvectors, Eigenvalues and Inverses Determining the equation for a matrix and confirming the inverse, eigenvalues Details: I have think the answer to question (a) is theta^2 [(1-p)I + pJ].

  • Linear Algebra : Rank and Signature of Quadratic Form

    So we need to find the characteristic polynomial of matrix A. The characteristic polynomial of matrix A, denoted by , is the following determinant.

  • Characteristic equation of a matrix and inverse of a matrix

    Characteristic equation of a matrix and inverse of a matrix.

  • Symplectic Matrix, Determinant, Characteristic Polynomial and Eigenvalues

    43664 Symplectic Matrix, Determinant, Characteristic Polynomial and Eigenvalues If ' is a symplectic matrix show that det ' = 1. Also prove that....where P(...) = det(,,,) is the characteristic polynomial of '.

  • Rotation matrices

    the eigenvalues set is: Solving Explicitly: The characteristic polynomial is: The eigenvalues are the solution of the solution of the polynomial: The solution discusses some of the properties of general rotation matrices and show they

  • Similarity Classes of 6x6 Polynomials

    So we only consider the Jordan canonical form of a matrix . It has the following Jordan canonical form: , where or is an matrix. We have . The characteristic polynomial of is . From the condition, we know this polynomial is .

View More Related Solutions