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diagonalizabl

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There are 13 letters in DIAGONALIZABL ( A1B3D2G2I1L1N1O1Z10 )

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Definitions of diagonalizabl in various dictionaries:

DIAGONALIZABL - In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P suc...

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Diagonalizabl might refer to
In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that Pāˆ’1AP is a diagonal matrix. If V is a finite-dimensional vector space, then a linear map T : V → V is called diagonalizable if there exists an ordered basis of V with respect to which T is represented by a diagonal matrix. Diagonalization is the process of finding a corresponding diagonal matrix for a Diagonalizable matrix or linear map. A square matrix that is not diagonalizable is called defective.
* Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle; once their eigenvalues and eigenvectors are known, one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power, and the determinant of a diagonal matrix is simply the product of all diagonal entries. Geometrically, a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling) — it scales the space, as does a homogeneous dilation, but by a different factor in each direction, determined by the scale factors on each axis (diagonal entries).
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