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>\ | + | *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-\ | + | *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-\ | + | *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>\ | + | *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.