Sentences with EIGENVECTOR
Check out our example sentences below to help you understand the context.Sentences
1
"The eigenvector of a matrix is a nonzero vector that only changes by a scalar factor when that matrix is applied to it."
2
"To find eigenvalues and eigenvectors, you need to solve the characteristic equation of the matrix."
3
"The eigenvector associated with the largest eigenvalue often carries the most important information about a system."
4
"In image processing, eigenvectors are used for dimensionality reduction and feature extraction."
5
"An eigenvector can be scaled up or down but cannot be changed in direction by a linear transformation."
6
"If a matrix has repeated eigenvalues, there may be multiple linearly independent eigenvectors associated with each eigenvalue."
7
"The eigenvectors of a symmetric matrix are always orthogonal to each other."
8
"The eigenvectors of a skew-symmetric matrix are orthogonal and purely imaginary."
9
"The eigenvector corresponding to the eigenvalue zero is called the null vector of the matrix."
10
"Eigenfaces are the eigenvectors of the covariance matrix of face image data."
11
"The principal component analysis (PCA) technique relies on eigenvectors to perform dimensionality reduction."
12
"The eigenvectors of a rotation matrix represent the axes of rotation."
13
"In quantum mechanics, eigenvectors of operators represent the possible states of a physical system."
14
"The eigenvector centrality measure is used in network analysis to identify important nodes in a network."
15
"Eigenvalues and eigenvectors provide valuable insights into the behavior of dynamic systems."
16
"The eigenvector equation Ax = λx relates the linear transformation A, the eigenvalue λ, and the eigenvector x."
17
"The stability of a linear control system can be analyzed using eigenvectors and eigenvalues."
1
"The eigenvector of a matrix A is a non-zero vector v such that Av is a scalar multiple of v."
2
"To find the eigenvectors of a matrix, we solve the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue, and I is the identity matrix."
3
"In linear algebra, eigenvectors have a wide range of applications, including in physics and computer science."
4
"The eigenvectors of a symmetric matrix are always orthogonal to each other."
5
"Eigenvalues and eigenvectors play a crucial role in the diagonalization of matrices."
6
"The eigenvectors of a Hermitian matrix are guaranteed to be orthogonal."
7
"When computing principal components in PCA, eigenvectors are used to represent the directions of maximum variance in the data."
8
"Given a square matrix A, the eigenvectors form a vector space called the eigenspace of A."
9
"In quantum mechanics, eigenvectors correspond to the possible states of a physical system."
10
"The eigenvectors of a linear transformation can help us understand how the transformation stretches or compresses different directions in space."
