Difference between revisions of "Manuals/calci/EIGENVALUES"

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*This function shows the Eigen value of the given matrix.
 
*This function shows the Eigen value of the given matrix.
 
*In <math>EIGENVALUES (Matrix)</math>,<math>Matrix</math> is any matrix values.
 
*In <math>EIGENVALUES (Matrix)</math>,<math>Matrix</math> 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.
+
*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 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>\lambda</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.   

Revision as of 06:49, 5 September 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 .
  • 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

Spreadsheet
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 
Spreadsheet
A B
1 5 6
2 9 -11

=EIGENVALUES(A1:B2)

-13.862780491200214 
7.8627804912002155
0.3031213645114406 0.9025310769284506
-0.9529519601620652 0.43062472662211493

See Also

References