|
|
|
|
|
Let $V$ be a vector space over $k$ and $T$ a linear operator on $V$ . An eigenvalue for $T$ is an scalar $\lambda$ (that is, an element of $k$ ) such that $T(z)=\lambda z$ for some nonzero vector $z\in V$ . Is that case, we also say that $z$ is an
eigenvector of $T$ .
This can also be expressed as follows: $\lambda$ is an eigenvalue for $T$ if the kernel of $A-\lambda I$ is non trivial.
A linear operator can have several eigenvalues (but no more than the dimension of the space). Eigenvectors corresponding to different eigenvalues are linearly independent.
|
"eigenvalue" is owned by drini. [ full author list (2) | owner history (2) ]
|
|
(view preamble | get metadata)
Cross-references: linearly independent, dimension, kernel, vector, scalar, eigenvalue, linear operator, vector space
There are 28 references to this entry.
This is version 5 of eigenvalue, born on 2003-10-15, modified 2004-06-03.
Object id is 5106, canonical name is EigenvalueOfALinearOperator.
Accessed 13987 times total.
Classification:
| AMS MSC: | 15A18 (Linear and multilinear algebra; matrix theory :: Eigenvalues, singular values, and eigenvectors) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
