Explore BrainMass

# Changing basis in order to diagonalize a matrix

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

https://brainmass.com/math/linear-algebra/changing-basis-order-diagonalize-matrix-10040

#### 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

\$2.49