Search for a tool
Eigenvalues of a Matrix

Tool to calculate eigenvalues of a matrix. The eigenvalues of a matrix are values that allow to reduce the associated endomorphisms.

Results

Eigenvalues of a Matrix -

Tag(s) : Matrix

Share dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Eigenvalues of a Matrix tool. Thank you.

# Eigenvalues of a Matrix

## Eigenvalues Calculator

Tool to calculate eigenvalues of a matrix. The eigenvalues of a matrix are values that allow to reduce the associated endomorphisms.

### What is an eigenvalue of a matrix? (Definition)

Eigenvalues are numbers that characterize a matrix. These numbers are important because, associated with their eigenvectors, they make it possible to express the matrix in a simpler form, which facilitates the calculations.

for any square matrix $M$ of size $m \times m$, eigenvalues are generally called lambda $\lambda$ and associated with an eigenvector $v$ if $$M.v = \lambda v \iff (M-\lambda I_m).v = 0$$ with $I_m$ the identity matrix (of size $m$).

Practically, the eigenvalues of $M$ are the roots of its characteristic polynomial $P$.

An eigenvalue of a matrix is always associated with an eigenvector. Use the eigenvectors calculator proposed by dCode.

### How to calculate eigen values of a matrix?

To find the eigenvalues of a matrix, calculate the roots of its characteristic polynomial.

Example: The 2x2 matrix $M=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$ has for characteristic polynomial $P(M) = x^2 − 4x − 5 = (x+1)(x-5)$. The roots of $P$ are found by the calculation $P(M)=0 \iff x= -1 \mbox{ or } x = 5$. The eigenvalues of the matrix $M$ are $-1$ and $5$.

NB : The eigenvector associated are $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ for $5$ and $\begin{bmatrix} -1 \\ 1 \end{bmatrix}$ for $-1$

### Why eigen- in eigenvalues?

Eigenvalues are called eigen because it is as German word which means proper, characteristic.

## Source code

dCode retains ownership of the source code of the script Eigenvalues of a Matrix online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Eigenvalues of a Matrix script for offline use on PC, iPhone or Android, ask for price quote on contact page !