EigenScopeStep 01
Eigenvalues
Meaning
Find eigenvalues
Eigenvalues are the scalars that keep a vector on the same line after A is applied.
Formula
det(A - lambda I) = 0The result panel lists every root found for the selected 2x2 or 3x3 matrix.
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CSS114 / Matrix Diagonalization
Matrix diagonalization analysis system for 2x2 and 3x3 matrices.
Now Interactive
2x2 / 3x3
Outputs
eigenvalues / eigenvectors / diagonalizable verdict / P^-1 A P
Live Workbench
The assignment flow is now usable: create a 2x2 or 3x3 matrix, calculate eigenvalues, eigenvectors, the diagonalization verdict, and the P, P^-1, D matrices when available.
Matrix Input
Sample cases
Editable matrix A
4 values
Analysis Output
Ready
Build A Matrix. Get The Algebra.
Choose 2x2 or 3x3, edit values, generate a sample, then calculate eigenvalues, eigenvectors, diagonalizability, P, P^-1, and D.
Project Overview
EigenScope turns the assignment into a readable sequence: enter a matrix, solve the characteristic equation, inspect the eigenvectors, then decide whether a diagonal form exists.
Target relation
D = P^-1 A P
The interface is organized around this relation: A is the input, P is the eigenvector basis, and D is the diagonal result when the basis is valid.
5-step tour
Step 01
Meaning
Eigenvalues are the scalars that keep a vector on the same line after A is applied.
Formula
det(A - lambda I) = 0The result panel lists every root found for the selected 2x2 or 3x3 matrix.
Step 02
Meaning
Eigenvectors are non-zero vectors that only scale when multiplied by A.
Formula
(A - lambda I)v = 0, v != 0Each eigenvalue is paired with an eigenvector basis when one is available.
Step 03
Meaning
A matrix is diagonalizable when it has enough independent eigenvectors to form a basis.
Formula
sum dim(E_lambda) = nThe report states whether the matrix is diagonalizable over the real or complex field.
Step 04
Meaning
P is built from independent eigenvectors, and D stores the matching eigenvalues.
Formula
D = P^-1 A PWhen valid, the report shows P, P^-1, and the diagonal matrix D.
Step 05
Meaning
Failure is usually caused by too few independent eigenvectors for the matrix size.
Formula
geometric multiplicity < algebraic multiplicityIf P cannot be formed, the report explains the missing eigenvector basis clearly.
Feature Outline
Computes eigenvalues and eigenvector bases for 2x2 and 3x3 matrices.
Checks whether enough independent eigenvectors exist to construct P.
Shows P, P^-1, and D when the matrix is diagonalizable.
Technical Stack
01
Next.js App Router
02
TypeScript
03
Tailwind CSS
04
MUI Theme
05
Framer Motion
06
Bun
Ready To Test