eigenvalue of a matrix (Meaning)
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
Synonyms & Antonyms of eigenvalue of a matrix
No Synonyms and anytonyms found
eigenvalue of a matrix Sentence Examples
- 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.
- 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.
- 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.
- The eigenvalues of a matrix can be used to determine the matrix's determinant, trace, and rank.
- The largest eigenvalue of a positive definite matrix is greater than zero, indicating the matrix's positive definiteness.
- The eigenvalues of a matrix can be used to determine the stability of a linear system described by the matrix.
- The eigenvalues of a matrix can be used to find the principal components of a multivariate dataset, enabling data reduction and visualization.
- 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
(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
No synonyms found.
No antonyms found.
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.
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.
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