Matrix Diagonalization Calculator
What is Matrix Diagonalization?
Matrix diagonalization is a process in linear algebra that transforms a square matrix into a diagonal matrix through similarity transformation. A diagonal matrix is a special matrix where all elements outside the main diagonal are zero. The process involves finding eigenvalues and eigenvectors of the original matrix.
When a matrix A is diagonalizable, it can be written as A = PDP⁻¹, where:
- D is a diagonal matrix containing the eigenvalues of A
- P is a matrix whose columns are the eigenvectors of A
- P⁻¹ is the inverse of P
How to Use Matrix Diagonalization Calculator
Step 1: Select Matrix Dimensions
Choose the size of your square matrix from the dropdown menu. Options include 2×2, 3×3, or 4×4 matrices.
Step 2: Enter Matrix Values
Input the numerical values for each cell in the matrix. Use decimal numbers if necessary.
Step 3: Review Input
Double-check all entered values to ensure accuracy before proceeding with calculation.
Step 4: Obtain Results
Press the calculate button to receive:
- The eigenvalues of your matrix
- The corresponding eigenvectors
- The diagonalized form
- Step-by-step explanation of the process
Step 5: Interpret Results
Examine the detailed solution, which includes the characteristic equation, eigenvalues, eigenvectors, and the final diagonalized form of your matrix.