eigenvalue of a square matrix Antonyms

No Synonyms and anytonyms found

Meaning of eigenvalue of a square matrix

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

(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.