Sentences with DIAGONALISABLE
Check out our example sentences below to help you understand the context.Sentences
1
"The matrix is diagonalisable."
2
"The linear transformation is diagonalisable."
3
"The diagonalisable matrix has distinct eigenvalues."
4
"The eigenvalues determine if a matrix is diagonalisable."
5
"The matrix is not diagonalisable if it has repeated eigenvalues."
6
"The matrix is not diagonalisable over the field of integers."
7
"The characteristic polynomial helps determine if a matrix is diagonalisable."
8
"The matrix is diagonalisable if it has a complete set of eigenvectors."
9
"The diagonalisable matrix can be represented as a diagonal matrix."
10
"The Jordan form of a matrix provides insight into its diagonalisable properties."
1
"A square matrix is diagonalisable if and only if it has n linearly independent eigenvectors."
2
"To check if a matrix is diagonalisable, we need to find its eigenvalues and eigenvectors."
3
"The matrix A is diagonalisable if it is similar to a diagonal matrix."
4
"A matrix is diagonalisable if and only if it has n distinct eigenvalues."
5
"If a matrix is diagonalisable, then its eigenvectors form a basis for its vector space."
6
"A diagonalisable matrix can be written as PDP^{-1}, where D is the diagonal matrix and P is the matrix of eigenvectors."
7
"Not all matrices are diagonalisable; some may have repeated eigenvalues or not enough linearly independent eigenvectors."
8
"The diagonalisable matrices are a proper subset of all square matrices."
9
"If a matrix is diagonalisable, it is always similar to itself."
10
"The set of diagonalisable matrices is closed under matrix addition and scalar multiplication."
11
"A matrix A is diagonalisable if and only if its characteristic polynomial splits completely."
12
"If the eigenvalues of a matrix are all distinct, then the matrix is diagonalisable."
13
"Every normal matrix is diagonalisable."
14
"The zero matrix is diagonalisable, but it does not have any eigenvalues."
15
"If a matrix A is diagonalisable, then its inverse A^{-1} is also diagonalisable."
16
"The identity matrix is always diagonalisable."
17
"If all the eigenvalues of a matrix are zero, then the matrix is diagonalisable."
18
"A diagonalisable matrix can be expressed as a sum of its eigenvalues multiplied by their corresponding eigenvectors."
19
"Similar matrices have the same eigenvalues, so if one of them is diagonalisable, the other must also be diagonalisable."
