[ahy-guh n-vek-ter] /ˈaɪ gənˌvɛk tər/
(maths, physics) a vector x satisfying an equation Ax = λx, where A is a square matrix and λ is a constant
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.
/German ˈaiɡər/ noun 1. a mountain in central Switzerland, in the Bernese Alps. Height: 3970 m (13 025 ft)
[eyt] /eɪt/ noun 1. a cardinal number, seven plus one. 2. a symbol for this number, as 8 or VIII. 3. a set of this many persons or things, as the crew of an eight-oared racing shell. 4. a playing card the face of which bears eight pips. 5. Informal. adjective 6. amounting to eight […]
- Eight-bit clean
software A term which describes a system that deals correctly with extended character sets which (unlike ASCII) use all eight bits of a byte. Many programs and communications systems assume that all characters have codes in the range 0 to 127. This leaves the top bit of each byte free for use as a parity […]
noun, Jewelry. 1. . noun, Jewelry. 1. a simple form of brilliant cut, having eight facets above and eight facets below the girdle, as well as the table, and usually a culet.