Similar Matrices and Quadratic Forms
To solve the quadratic form, consider the matrix ( A = \begin{bmatrix} 0 & 1 & 1 & -1 \ 1 & 0 & -1 & 1 \ 1 & -1 & 0 & 1 \ -1 & 1 & 1 & 0 \end{bmatrix} ). Use the following code to calculate the eigenvalues and eigenvectors:
A = [0, 1, 1, -1; 1, 0, -1, 1; 1, -1, 0, 1; -1, 1, 1, 0];
[P, D] = eig(A);
Here, P is the matrix of eigenvectors, and D is the diagonal matrix of eigenvalues. These values are crucial for solving quadratic forms and understanding the properties of similar matrices.