eigenvalue of a square matrix Synonyms

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eigenvalue of a square matrix Meaning

Wordnet

eigenvalue of a square 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 square matrix Sentence Examples

1. The eigenvalues of a square matrix are the values that, when substituted into the characteristic equation, result in a determinant of zero.
2. The eigenvalues of a symmetric matrix are all real.
3. The eigenvalues of a Hermitian matrix are all real.
4. The eigenvalues of a skew-symmetric matrix are all purely imaginary.
5. The determinant of a matrix is equal to the product of its eigenvalues.
6. The trace of a matrix is equal to the sum of its eigenvalues.
7. The rank of a matrix is equal to the number of its nonzero eigenvalues.
8. The nullity of a matrix is equal to the number of its zero eigenvalues.
9. The eigenvectors of a matrix are the nonzero vectors that, when multiplied by the matrix, are scaled by the corresponding eigenvalue.
10. The eigenspaces of a matrix are the subspaces of the vector space on which the matrix acts that are spanned by the eigenvectors corresponding to a given eigenvalue.

FAQs About the word eigenvalue of a square matrix

What is the meaning of the word eigenvalue of a square 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 square matrix

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What are the antonyms of the word eigenvalue of a square matrix

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What is the usage of word eigenvalue of a square matrix

The eigenvalues of a square matrix are the values that, when substituted into the characteristic equation, result in a determinant of zero.

The eigenvalues of a symmetric matrix are all real.

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

The eigenvalues of a Hermitian matrix are all real.

The eigenvalues of a skew-symmetric matrix are all purely imaginary.