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The Frobenius norm is sub-multiplicative and is very useful for numerical linear algebra.
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A state with respect to a C*-algebra is a positive linear functional over it with unit norm.
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A Kleinian group Γ is called arithmetic if it is commensurable with the group norm 1 elements of an order of quaternion algebra A ramified at all real places over a number field k with exactly one complex place.
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The prototypical example of a C*-algebra is the algebra B(H) of bounded (equivalently continuous) linear operators defined on a complex Hilbert space H; here x* denotes the adjoint operator of the operator x : H → H. In fact, every C*-algebra, A, is *-isomorphic to a norm-closed adjoint closed subalgebra of B(H) for a suitable Hilbert space, H; this is the content of the Gelfand–Naimark theorem.
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The algebra M(n, C) of n × n matrices over C becomes a C*-algebra if we consider matrices as operators on the Euclidean space, Cn, and use the operator norm ||·|| on matrices.
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An application of this theorem is the result that every class in the ideal class group of a number field K contains an integral ideal of norm not exceeding a certain bound, depending on K, called Minkowski's bound: the finiteness of the class number of an algebraic number field follows immediately.
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To design controllers, three different techniques of control are used; based control minimum norm, linear algebra-based control and sliding mode control. The control systems designed and simulated using MATLAB and SIMULINK. a performance comparison between controllers through integral absolute error index IAE is made. tests are performed using controllers designed in the dynamic model of mobile manipulator.
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Bounded linear operators over Banach space form a Banach algebra in respect to the standard operator norm.
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In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.
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In analogy with the case of the algebraic double dual, there is always a naturally defined continuous linear operator V → V′′ from a normed space V into its continuous double dual V′′, defined by
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10 sinne gevind in 4 ms. Hulle kom uit baie bronne en word nie nagegaan nie.