Table of contents: What is a matrix? Diagonal matrix: definition and properties Eigenvalues and eigenvectors How to diagonalize a matrix? Example: using the diagonalize matrix calculatorWelcome to the diagonaliz
The matrix A = \begin{bmatrix} 3 & -13\ 5 & 1\ \end{bmatrix} has eigenvalues r_1 = 2 + 8i and r_2 = 2 - 8i, and corresponding eigenvectors \xi^{(1)} = \begin{bmatrix} 1 + 8i\ 5 \end{bmatrix} and \x...
It turns out to be easier than I thought. Given V such that A*V=V*E we find any W such that [W,V] is invertible and if A*W = W*F+V*G (i.e. [W,V]\A*[W,V] = [E,0;F,G] then setting U=W-V*X we solve the Sylvester equation E*X-X*F=G using lyap() and [U...
Finding a diagonal matrix can be a lengthy process, but it’s easy if you know the steps! You’ll need to calculate the eigenvalues, get the eigenvectors for those values, and use the diagonalization equation. Diagonal matrices are great for many different operations, such as computing the po...