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Anwendungsbeispiele Englisch
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- Some of the properties of inverse matrices are shared by generalized inverses (for example, the Moore–Penrose inverse), which can be defined for any "m"-by-"n" matrix.
- The matrix ("X"T "X")–1 "X"T="Q" "X"T is called the Moore–Penrose pseudoinverse matrix of X.
- No rank deficient matrix has any (even one-sided) inverse. However, the Moore–Penrose inverse exists for all matrices, and coincides with the left or right (or true) inverse when it exists.
- Both MATLAB and GNU Octave natively support linear algebra operations such as matrix multiplication, matrix inversion, and the numerical solution of system of linear equations, even using the Moore–Penrose pseudoinverse.
- with its Moore–Penrose inverse (pseudoinverse).
- stands for the Moore–Penrose pseudoinverse. This is just one of many ways to construct the projection operator.
- is known as the Moore–Penrose pseudoinverse of "X".
- For the case where [...] is not invertible the Moore–Penrose pseudoinverse should be used instead.
- A whitening operator can be then defined from the factorization of the Moore–Penrose inverse of the covariance operator, which has effective mapping on Karhunen–Loève type expansions of [...].
- is a Moore-Penrose pseudoinverse. After this update [...] is renormalized to fit the constraints and the new sparse coding is obtained again.
- If "H"11 is singular, we can still define the generalized Schur complement, using the Moore–Penrose inverse [...] instead of [...].
- One motivation for studying these semigroups is that they allow generalizing the Moore–Penrose inverse's properties from [...] and [...] to more general sets.
- In order to solve more general least-squares problems, one can define Moore–Penrose inverses for all continuous linear operators [...] between two Hilbert spaces [...] and [...] , using the same four conditions as in our definition above.
© dict.cc English-German dictionary 2024
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