Example of a matrix diagonalization Step 1: Find the characteristic polynomial Step 2: Find the eigenvalues Step 3: Find the eigenspaces Step 4: Determine linearly independent eigenvectors

In this video I show how to calculate the eigenvalues and eigenvectors of a 2x2 matrix A, and show how to find a diagonal matrix D and an invertible matrix P such that A =

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Since the 2 × 2 matrix A has two distinct eigenvalues, it is diagonalizable. To find the invertible matrix S, we need eigenvectors. Let us find the eigenvectors corresponding to the

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Diagonalize the Upper Triangular Matrix and Find the Power of the Matrix Consider the $2\times 2$ complex matrix \[A=\begin{bmatrix} a & b-a\\ 0& b \end{bmatrix}.\] (a) Find the eigenvalues

Diagonalisation of a 2x2 matrix leading to the diagonal factorisation of a 2x2 matrix. Using the diagonal factorisation of a 2x2 matrix to find a power of the matrix.

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