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diagona
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There are 7 letters in DIAGONA ( A1D2G2I1N1O1 )
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Definitions of diagona in various dictionaries:
DIAGONA - 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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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 Pā1AP is a diagonal matrix. If V is a finite-dimensional vector space, then a linear map T : V ā 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) ā 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). |