eigenvalue of a matrix Synonyms

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eigenvalue of a matrix Meaning

Wordnet

eigenvalue of a matrix (n)

(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant

eigenvalue of a matrix Sentence Examples

1. The eigenvalues of a matrix are the roots of its characteristic polynomial.
2. The eigenvectors of a matrix are the non-zero vectors that are preserved by the matrix's linear transformation, except for a scalar factor known as the eigenvalue.
3. The eigenvalues of a matrix determine the intrinsic properties of the matrix, such as its stability and its classification as diagonalizable or non-diagonalizable.
4. The eigenvalues of a real symmetric matrix are always real and form a complete set of orthogonal eigenvectors, making it diagonalizable.
5. The eigenvalues of a complex matrix are not necessarily real, and its eigenvectors may not form a complete set, resulting in a need for generalized eigenvectors for diagonalization.
6. The eigenvalues of a matrix can be used to determine the matrix's determinant, trace, and rank.
7. The largest eigenvalue of a positive definite matrix is greater than zero, indicating the matrix's positive definiteness.
8. The eigenvalues of a matrix can be used to determine the stability of a linear system described by the matrix.
9. The eigenvalues of a matrix can be used to find the principal components of a multivariate dataset, enabling data reduction and visualization.
10. The eigenvalues of a matrix can be used in various fields, including linear algebra, quantum mechanics, and engineering, to understand the behavior of systems governed by matrices.

FAQs About the word eigenvalue of a matrix

What is the meaning of the word eigenvalue of a matrix

(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant

What are the synonyms of the word eigenvalue of a matrix

No synonyms found.

What are the antonyms of the word eigenvalue of a matrix

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What is the usage of word eigenvalue of a matrix

The eigenvalues of a matrix are the roots of its characteristic polynomial.

The eigenvectors of a matrix are the non-zero vectors that are preserved by the matrix's linear transformation, except for a scalar factor known as the eigenvalue.

How to use the word eigenvalue of a matrix in a sentence?

The eigenvalues of a matrix determine the intrinsic properties of the matrix, such as its stability and its classification as diagonalizable or non-diagonalizable.

The eigenvalues of a real symmetric matrix are always real and form a complete set of orthogonal eigenvectors, making it diagonalizable.