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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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.