Manuals/calci/EIGENVALUES
EIGENVALUES (Matrix)
- 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 Matrix} is the array of numeric elements.
Description
- This function shows the Eigen value of the given matrix.
- In 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 EIGENVALUES (Matrix)} ,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 Matrix} 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 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 \lambda} 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 \lambda} 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 (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 (A-\lambda.I).v=0} .
- If v is non-zero, this equation will only have a solution if 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 |A-\lambda.I|.v=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.
Examples
| 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 |
| A | B | |
|---|---|---|
| 1 | 5 | 6 |
| 2 | 9 | -11 |
=EIGENVALUES(A1:B2)
-13.862780491200214 |
7.8627804912002155 |
0.3031213645114406 0.9025310769284506 |
-0.9529519601620652 0.43062472662211493 |