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>\Lamda</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|.v=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.
 +
 +
==Examples==
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C   
 +
|-
 +
! 1
 +
| 3 || 7 || 5
 +
|-
 +
! 2
 +
| 10 || 12 || 8
 +
|-
 +
!3
 +
| 6 || 8 || 14
 +
|}
 +
=EIGENVALUES(A1:C3)
 +
{| border="1" cellpadding="5" cellspacing="0"
 +
|-
 +
|
 +
-2.018987498930866
 +
||
 +
25.303239119591886
 +
||
 +
5.715748379338994
 +
|-
 +
||
 +
-0.8195524172935329 0.3557792393359474 0.2128903683040517
 +
||
 +
0.5726193656991498 0.663334322125492 0.6212592923173481
 +
||
 +
  0.02099755544415341 0.6583378387635402 -0.7541316747045657
 +
|}
 +
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B   
 +
|-
 +
! 1
 +
| 5 || 6
 +
|-
 +
! 2
 +
| 9 || -11
 +
|}
 +
=EIGENVALUES(A1:B2)
 +
{| border="1" cellpadding="5" cellspacing="0"
 +
|-
 +
|
 +
-13.862780491200214
 +
||
 +
7.8627804912002155
 +
|-
 +
|
 +
0.3031213645114406 0.9025310769284506
 +
|| 
 +
-0.9529519601620652 0.43062472662211493
 +
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|v=PhfbEr2btGQ|280|center|Eigen Values}}
 +
 +
==See Also==
 +
*[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]]
 +
*[[Manuals/calci/CONFERENCE| CONFERENCE]]
 +
*[[Manuals/calci/PASCAL| PASCAL]]
 +
 +
==References==
 +
*[http://lpsa.swarthmore.edu/MtrxVibe/EigMat/MatrixEigen.html  Eigen Values]
 +
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 13:58, 25 April 2019

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

Related Videos

Eigen Values

See Also

References

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