Explore BrainMass
Share

Explore BrainMass

    Changing basis in order to diagonalize a matrix

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Suppose that the matrix A is a linear operator on R(2) represented in the standard basis {i,j}, by the matrix
    mat(A)= [-1 3;2 4].

    Find a new basis in which A is diagonalized.

    © BrainMass Inc. brainmass.com October 9, 2019, 3:40 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/changing-basis-order-diagonalize-matrix-10040

    Attachments

    Solution Preview

    See attachment for a step-by-step solution using a 2x2 matrix as an example used to illustrate the process.

    Diagonalize A
    So, the first step in solving this problem is to solve the mini- problem of det(A-lamda*I)=0
    This will yield the eigenvalues of A.
    Next, we need to find the eigenvectors ...

    Solution Summary

    A step-by-step solution is provided which illustrates how to change basis while diagonalizing a matrix. A 2x2 matrix is used as an example

    $2.19