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