# Manuals/calci/EIGENVALUES

EIGENVALUES (Matrix)

• is the array of numeric elements.

## Description

• This function shows the Eigen value of the given matrix.
• In , is any matrix values.
• In linear algebra, an eigen vector or characteristic vector of a linear transformation is a non-zero vector whose direction does not change when that linear transformation is applied to it.
• Let A be a linear transformation represented by a matrix A.
• Let A is an nxn matrix, v is a non zero nx1 vector and is a scalar which may be either real or complex.
• Any value of for which this equation has a solution is known as an eigenvalue of the matrix A.
• It is sometimes also called the characteristic value.
• The vector, v, which corresponds to this value is called an eigenvector.
• The eigenvalue problem can be rewritten as .
• If v is non-zero, this equation will only have a solution if .
• This equation is called the characteristic equation of A, and is an nth order polynomial in with n roots.
• These roots are called the eigenvalues of A.

## Examples

A B C
1 3 7 5
2 10 12 8
3 6 8 14

=EIGENVALUES(A1:C3)

 -2.018987498930866  25.303239119591886  5.715748379338994  -0.8195524172935329 0.3557792393359474 0.2128903683040517  0.5726193656991498 0.663334322125492 0.6212592923173481   0.02099755544415341 0.6583378387635402 -0.7541316747045657 
A B
1 5 6
2 9 -11

=EIGENVALUES(A1:B2)

 -13.862780491200214  7.8627804912002155  0.3031213645114406 0.9025310769284506  -0.9529519601620652 0.43062472662211493 

Eigen Values