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

Eigenvalues of a Matrix - dCode

Tag(s) : Matrix

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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

To calculate eigenvalues, take a square matrix \( M \) of size \( m \times m \), the eigenvalues of \( M \) are the roots of the characteristic polynomial \( P \) of the matrix \( M \).

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 \( m \)).

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

Example: $$ M=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix} \Rightarrow P(M) = x^2 − 4x − 5 = (x+1)(x-5) $$

Example: The 2x2 matrix $$ P(M)=0 \iff x= -1 \mbox{ or } x = 5 $$ The eigenvalues of the matrix \( M \) are \( -1 \) and \( 5 \). And the eigenvector associated are \( \begin{bmatrix} 1 \\ 2 \end{bmatrix} \) for \( 5 \) and \( \begin{bmatrix} -1 \\ 1 \end{bmatrix} \) for \( -1 \).

Normally the definition of the eigenvector exclude the zero vector. However, if there are not as many independent eigenvectors as eigenvalues, dCode will display a null vector.

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

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 given 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 !

eigenvalue,matrix,eigenvector,space,characteristic

Source : https://www.dcode.fr/matrix-eigenvalues

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback