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
Synonyms & Antonyms of eigenvalue of a square matrix
No Synonyms and anytonyms found
eigenvalue of a square matrix Sentence Examples
- 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.
- The eigenvalues of a Hermitian matrix are all real.
- The eigenvalues of a skew-symmetric matrix are all purely imaginary.
- The determinant of a matrix is equal to the product of its eigenvalues.
- The trace of a matrix is equal to the sum of its eigenvalues.
- The rank of a matrix is equal to the number of its nonzero eigenvalues.
- The nullity of a matrix is equal to the number of its zero eigenvalues.
- The eigenvectors of a matrix are the nonzero vectors that, when multiplied by the matrix, are scaled by the corresponding eigenvalue.
- 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
(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 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.
The eigenvalues of a Hermitian matrix are all real.
The eigenvalues of a skew-symmetric matrix are all purely imaginary.
