Examples of 'diagonalizable' in a sentence
Meaning of "diagonalizable"
Diagonalizable (adjective): Refers to a square matrix that can be converted into a diagonal matrix through a similarity transformation. This property is useful in various mathematical and scientific applications
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- Able to be diagonalized.
How to use "diagonalizable" in a sentence
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diagonalizable
A matrix that is not diagonalizable is said to be defective.
Has only real eigenvalues and is diagonalizable.
Only diagonalizable matrices can be factorized in this way.
The torsion subgroup of a diagonalizable group is dense.
Is diagonalizable by an orthogonal matrix.
A square matrix that is not diagonalizable is called defective.
Diagonalizable matrices are of particular interest since matrix functions of them can be computed easily.
Such linear transformations are called diagonalizable.
The only nilpotent diagonalizable matrix is the zero matrix.
Show that each of these is diagonalizable.
Note that only diagonalizable matrices can be factorized in this way.
But not all matrices are diagonalizable.
Notice that a matrix is diagonalizable if and only if it is similar to a diagonal matrix.
Such matrices are said to be diagonalizable.
The permeability tensor is always diagonalizable being both symmetric and positive definite.
See also
A scaling in the most general sense is any affine transformation with a diagonalizable matrix.
He discovered the diagonalizable matrix.
Hence they are diagonalizable and their eigenvectors for distinct eigenvalues must be orthogonal.
Some real matrices are not diagonalizable over the reals.
One can show that A is normal if and only if it is unitarily diagonalizable.
Note that a real symmetric matrix is diagonalizable by an orthogonal matrix.
The family of Hermitian matrices is a proper subset of matrices that are unitarily diagonalizable.
In particular they are orthogonally diagonalizable and their eigenvalues are real.
Such a matrix A is said to be similar to the diagonal matrix Λ or diagonalizable.
Theorem A matrix is orthogonally diagonalizable if and only if it is symmetric.
Has s distinct real eigenvalues, it follows that it is diagonalizable.
Proposition . is diagonalizable if and only if it is similar to a diagonal matrix.
Diagonalization is the process of finding a corresponding diagonal matrix for a diagonalizable matrix or linear map.
Hence, a matrix is diagonalizable if and only if its nilpotent part is zero.
In fact the tensor A is always diagonalizable.
An idempotent matrix is always diagonalizable and its eigenvalues are either 0 or 1.
In this case, the endomorphism and the matrix are said diagonalizable.
In chapter 1 we learned that diagonalizable linear transformations are the easiest to use.
Hence, this matrix is not diagonalizable.
Some matrices are not diagonalizable over any field, most notably nonzero nilpotent matrices.
Because, given a quadratic form, there is a basis where its matrix is diagonalizable.
In the language of Lie theory, a set of simultaneously diagonalizable matrices generate a toral Lie algebra.
If a complex n × n matrix A has n distinct complex eigenvalues, then it is diagonalizable.
Definition, A square matrix A is said to be diagonalizable if it is similar to a diagonal matrix.
By iteration it follows that all B-s are simultaneously diagonalizable.
A method for finding in A for a diagonalizable matrix A is the following:.
If A can be written in this form, it is called diagonalizable.
Then, is diagonalizable.
And therefore if k = n then A is diagonalizable.
For instance, the matrices, formula 11are diagonalizable but not simultaneously diagonalizable because they do not commute.
Conversely, suppose a matrix A is diagonalizable.
For example, " A " is called diagonalizable if it is similar to a diagonal matrix.
If the operator is orthogonal ( an orthogonal involution ), it is orthonormally diagonalizable.
A compact normal operator ( in particular, a normal operator on a finite-dimensional linear space ) is unitarily diagonalizable.
In this extended sense, if the characteristic polynomial is square-free, then the matrix is diagonalizable.
