Manuals/calci/EIGENVALUES

EIGENVALUES (Matrix)

• $Matrix$ is the array of numeric elements.

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 Failed to parse (unknown function "\Lamda"): {\displaystyle \Lamda} is a scalar which may be either real or complex.
• Any value of Failed to parse (unknown function "\Lamda"): {\displaystyle \Lamda} 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 Failed to parse (unknown function "\Lamda"): {\displaystyle (A-\Lamda.I).v=0} .
• If v is non-zero, this equation will only have a solution if Failed to parse (unknown function "\Lamda"): {\displaystyle |A-\Lamda·I|=0} .
• This equation is called the characteristic equation of A, and is an nth order polynomial in Failed to parse (unknown function "\Lamda"): {\displaystyle \Lamda} with n roots.
• These roots are called the eigenvalues of A.