| slovo | definícia |
eigen
(wn) | Eigen
n 1: German chemist who did research on high-speed chemical
reactions (born in 1927) [syn: Eigen, Manfred Eigen] |
| | podobné slovo | definícia |
eigenvalue
(encz) | eigenvalue,vlastní číslo [mat.] vlastní číslo matice nebo lineárního
operátoru MM |
eigenvalues
(encz) | eigenvalues,vlastní hodnoty Zdeněk Brož |
eigenvector
(encz) | eigenvector,vlastní vektor Zdeněk Brož |
eigen
(wn) | Eigen
n 1: German chemist who did research on high-speed chemical
reactions (born in 1927) [syn: Eigen, Manfred Eigen] |
eigenvalue
(wn) | eigenvalue
n 1: (mathematics) any number such that a given square matrix
minus that number times the identity matrix has a zero
determinant [syn: eigenvalue, eigenvalue of a matrix,
eigenvalue of a square matrix, {characteristic root of a
square matrix}] |
eigenvalue of a matrix
(wn) | eigenvalue of a matrix
n 1: (mathematics) any number such that a given square matrix
minus that number times the identity matrix has a zero
determinant [syn: eigenvalue, eigenvalue of a matrix,
eigenvalue of a square matrix, {characteristic root of a
square matrix}] |
eigenvalue of a square matrix
(wn) | eigenvalue of a square matrix
n 1: (mathematics) any number such that a given square matrix
minus that number times the identity matrix has a zero
determinant [syn: eigenvalue, eigenvalue of a matrix,
eigenvalue of a square matrix, {characteristic root of a
square matrix}] |
manfred eigen
(wn) | Manfred Eigen
n 1: German chemist who did research on high-speed chemical
reactions (born in 1927) [syn: Eigen, Manfred Eigen] |
eigenvalue
(foldoc) | eigenvalue
The factor by which a linear transformation
multiplies one of its eigenvectors.
(1995-04-10)
|
eigenvector
(foldoc) | eigenvector
A vector which, when acted on by a particular
linear transformation, produces a scalar multiple of the
original vector. The scalar in question is called the
eigenvalue corresponding to this eigenvector.
It should be noted that "vector" here means "element of a
vector space" which can include many mathematical entities.
Ordinary vectors are elements of a vector space, and
multiplication by a matrix is a linear transformation on
them; smooth functions "are vectors", and many partial
differential operators are linear transformations on the space
of such functions; quantum-mechanical states "are vectors",
and observables are linear transformations on the state
space.
An important theorem says, roughly, that certain linear
transformations have enough eigenvectors that they form a
basis of the whole vector states. This is why {Fourier
analysis} works, and why in quantum mechanics every state is a
superposition of eigenstates of observables.
An eigenvector is a (representative member of a) fixed point
of the map on the projective plane induced by a {linear
map}.
(1996-09-27)
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