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Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:}. where denotes the supremum.
Maximum firing range. 100–200 km (120 mi) [1][2] Engine. diesel. Payload capacity. ~ 75 kg TNT equivalent (estimate) Suspension. 6x6 wheeled. The KN-09 (K-SS-X-9) [3] is a North Korean 300 mm rocket artillery system of a launcher unit comprising eight rockets packaged in two four-rocket pods.
The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, below ...
Normal operator. In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N : H → H that commutes with its Hermitian adjoint N*, that is: NN* = N*N. [1] Normal operators are important because the spectral theorem holds for them. The class of normal operators is well understood.
Operator norm. In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Informally, the operator norm of a linear map is the maximum factor by which it ...
In mathematics, the Smith normal form (sometimes abbreviated SNF [1]) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right by invertible square ...
Normed vector spaces are a superset of inner product spaces and a subset of metric spaces, which in turn is a subset of topological spaces. In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. [1] A norm is a generalization of the intuitive notion of "length" in the ...
Theorem— Let X be a Banach space, C be a compact operator acting on X, and σ (C) be the spectrum of C. Every nonzero λ ∈ σ (C) is an eigenvalue of C. For all nonzero λ ∈ σ (C), there exist m such that Ker ( (λ − C) m) = Ker ( (λ − C) m+1), and this subspace is finite-dimensional. The eigenvalues can only accumulate at 0.