Sentences with EIGENVECTORS

"The eigenvectors of a diagonal matrix are just the standard basis vectors."

"To find the eigenvectors of a matrix, one typically solves a system of linear equations."

"The eigenvectors of a symmetric matrix are always orthogonal to each other."

"When a matrix has repeated eigenvalues, there can be multiple linearly independent eigenvectors for each eigenvalue."

"The eigenvectors of a unitary matrix form an orthonormal basis."

"The eigenvectors corresponding to distinct eigenvalues of a matrix are always linearly independent."

"The eigenvectors of a Hermitian matrix are always real."

"Eigenvalue decomposition factorizes a square matrix into a diagonal matrix of eigenvalues and a matrix of eigenvectors."

"The eigenvectors of a projection matrix are always either 0 or 1."

"The eigenvectors of a reflection matrix are the vectors that are left unchanged by the reflection."

"In quantum mechanics, the eigenvectors of an operator represent the state vectors of the system."

"The eigenvectors of a linear transformation determine its stretch and compression factors in each direction."

"Eigenvectors can be scaled by any non-zero scalar and still remain eigenvectors."

"A singular matrix does not have any non-zero eigenvectors."

"The eigenvectors of a positive definite matrix are always positive."

"The eigenvectors of the identity matrix are the standard basis vectors."

"A matrix is diagonalizable if it has a full set of linearly independent eigenvectors."