(physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Used in a Sentence
eigenvectors
Definitions, parts of speech, synonyms, and sentence examples for eigenvectors.
Editorial note
The advantage is that eigenvectors can be specified by coordinates, so you can find them by computational methods.
Examples16
Definitions2
Parts of speech1
Quick take
(physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
Meaning at a glance
The clearest senses and uses of eigenvectors gathered in one view.
(linear algebra) A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
Definitions
Core meanings and parts of speech for eigenvectors.
noun
(physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
noun
(linear algebra) A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
Example sentences
The advantage is that eigenvectors can be specified by coordinates, so you can find them by computational methods.
So the eigenvectors are like the directions that describe position of an airplane: roll pitch and yaw.
To make a mathematical analogy, the first few eigenvectors can capture most of the information about a data set.
There is a huge gap between the first part explaining vectors and then the part explaining eigenvectors.
If you can do a decent treatment of eigenvectors in a non-honors freshman course, my hat goes off to you.
And while they're very important, eigenvectors are still a shadow of the historico-cultural impact of calculus.
Quantum mechanics, for example, is dedicated to finding the eigenvalues and eigenvectors of the Hamiltonian.
Sure, there will be people who will have to know about eigenvectors tomorrow - but do we all?
It's a two-dimensional plot, with two-dimensional vectors, and the number of eigenvectors is two.
You just might learn about eigenvectors and invent the next PageRank!
I have no idea what eigenvectors or eigenvalues are, so this just confused me more.
Well, the number of families of eigenvectors; the number of colours.
Quote examples
Defective matrices still have eigenvalues and eigenvectors, but they are non-unique or incomplete in some way that makes the transformation "confusable".
My take: The eigenvectors are the “axes” of the transformation represented by the matrix.
Lagrange realized that the principal axes are the eigenvectors of the inertia matrix".
So, first off, you can get this whole result much faster if you know what "linearity" is (and while your average HNer might not, anyone who knows what eigenvectors are should).
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use eigenvectors in a sentence?
The advantage is that eigenvectors can be specified by coordinates, so you can find them by computational methods.
What does eigenvectors mean?
(physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
What part of speech is eigenvectors?
eigenvectors is commonly used as noun.