Sentences with DIAGONALIZABLE
Check out our example sentences below to help you understand the context.Sentences
1
"The matrix A is diagonalizable."
2
"A square matrix with distinct eigenvalues is always diagonalizable."
3
"The diagonalizable matrix can be written as A = PDP^(-1), where D is a diagonal matrix."
4
"If a matrix is not diagonalizable, it is called defective."
5
"The matrix A is diagonalizable if and only if it has a complete set of eigenvectors."
6
"Hermitian matrices are always diagonalizable."
7
"The matrix A is diagonalizable over the field F if there exists an invertible matrix P and a diagonal matrix D such that A = PDP^(-1)."
8
"The matrix A is diagonalizable if it is similar to a diagonal matrix."
9
"Some matrices are not diagonalizable over certain fields."
10
"A Jordan block with size greater than 1 is not diagonalizable."
1
"A matrix is diagonalizable if it can be transformed into a diagonal matrix by similarity."
2
"The matrix A is diagonalizable if and only if it has n linearly independent eigenvectors."
3
"We can determine if a matrix is diagonalizable by checking if it has n distinct eigenvalues."
4
"The diagonalizable property of a matrix is often used in linear algebra."
5
"A diagonalizable matrix can be easily raised to a power by raising its eigenvalues to that power."
6
"The diagonalizable property of a matrix allows for simpler calculations in certain contexts."
7
"Finding the eigenvectors of a matrix is an important step in determining if it is diagonalizable."
8
"Any matrix with distinct eigenvalues is diagonalizable."
9
"The diagonalizable property is closely related to the concept of eigenvectors and eigenvalues."
10
"Not all matrices are diagonalizable; some matrices have repeated eigenvalues."
11
"A diagonalizable matrix can be written as a product of three matrices: P, D, and P inverse."
12
"If a matrix is diagonalizable, it can be expressed as A = PDP^(-1), where D is a diagonal matrix."
13
"A matrix is diagonalizable if and only if its minimal polynomial is a product of distinct linear factors."
14
"A symmetric matrix is always diagonalizable."
15
"The diagonalizable property simplifies computations involving matrix exponentiation."
16
"In certain applications, it is desirable to have a diagonalizable matrix rather than a non-diagonalizable one."
17
"A matrix is diagonalizable over the field F if and only if it has a full set of n linearly independent eigenvectors."
18
"The diagonalizable property of a matrix can be generalized to other algebraic structures."
19
"The diagonalizable property is useful in analyzing the behavior of linear systems."
