Manuals/calci/EIGENVALUES

EIGENVALUES (Matrix)

Description

This function shows the Eigen value of the given matrix.
In $EIGENVALUES(Matrix)$ , $Matrix$ 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 $\lambda$ is a scalar which may be either real or complex.
Any value of $\lambda$ 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 $(A-\lambda .I).v=0$ .
If v is non-zero, this equation will only have a solution if $|A-\lambda .I|.v=0$ .
This equation is called the characteristic equation of A, and is an nth order polynomial in $\lambda$ with n roots.
These roots are called the eigenvalues of A.

1. EIGENVALUES([[3,7,5],[10,12,8],[6,8,14]])

Result
-2.018987498930866	25.303239119591886	5.715748379338994
-0.8195524172935329 0.3557792393359474 0.2128903683040517	0.5726193656991498 0.663334322125492 0.6212592923173481	0.02099755544415341 0.6583378387635402 -0.7541316747045657

2. EIGENVALUES([[5,6],[9,-11]])

Result
-13.862780491200214	7.8627804912002155
0.3031213645114406 0.9025310769284506	-0.9529519601620652 0.43062472662211493