Difference between revisions of "Manuals/calci/EIGENVALUES"

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*Let A be a linear transformation represented by a matrix A.
 
*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 <math>\lambda</math> is a scalar which may be either real or complex.
 
*Let A is an nxn matrix,v is a non zero nx1 vector and <math>\lambda</math> is a scalar which may be either real or complex.
*Any value of <math>\Lamda</math> for which this equation has a solution is known as an eigenvalue of the matrix A.   
+
*Any value of <math>\lambda</math> for which this equation has a solution is known as an eigenvalue of the matrix A.   
 
*It is sometimes also called the characteristic value.   
 
*It is sometimes also called the characteristic value.   
 
*The vector, v, which corresponds to this value is called an eigenvector.   
 
*The vector, v, which corresponds to this value is called an eigenvector.   
*The eigenvalue problem can be rewritten as <math>(A-\Lamda.I).v=0</math>.
+
*The eigenvalue problem can be rewritten as <math>(A-\lambda.I).v=0</math>.
*If v is non-zero, this equation will only have a solution if <math>|A-\Lamda·I|=0</math>.
+
*If v is non-zero, this equation will only have a solution if <math>|A-\lambda·I|=0</math>.
*This equation is called the characteristic equation of A, and is an nth order polynomial in <math>\Lamda</math> with n roots.   
+
*This equation is called the characteristic equation of A, and is an nth order polynomial in <math>\lambda</math> with n roots.   
 
*These roots are called the eigenvalues of A.
 
*These roots are called the eigenvalues of A.

Revision as of 16:39, 11 July 2017

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 Failed to parse (syntax error): {\displaystyle |A-\lambda·I|=0} .
  • 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.