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However, every finite dimensional normed space is a reflexive Banach space, so Riesz’s lemma does holds for = when the normed space is finite-dimensional, as will now be shown. When the dimension of X {\displaystyle X} is finite then the closed unit ball B ⊆ X {\displaystyle B\subseteq X} is compact.
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. [ 1 ] [ 2 ] This method is particularly valuable in scenarios where the number of inputs to a system is substantial enough to make exhaustive testing impractical.
The Cotlar–Stein almost orthogonality lemma is a mathematical lemma in the field of functional analysis. It may be used to obtain information on the operator norm on an operator , acting from one Hilbert space into another, when the operator can be decomposed into almost orthogonal pieces.
The norm on induced by , is equal to the original norm on and the continuous dual space of is the set of all real-valued bounded -linear functionals on (see the article about the polarization identity for additional details about this relationship).
Entire test suites or test cases exposing real bugs can be automatically generated by software using model checking or symbolic execution.Model checking can ensure all the paths of a simple program are exercised, while symbolic execution can detect bugs and generate a test case that will expose the bug when the software is run using this test case.
It is associated with simplicity; the more orthogonal the design, the fewer exceptions. This makes it easier to learn, read and write programs in a programming language [citation needed]. The meaning of an orthogonal feature is independent of context; the key parameters are symmetry and consistency (for example, a pointer is an orthogonal concept).
In finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis) of an orthogonal transformation is an orthogonal matrix. Its rows are mutually orthogonal vectors with unit norm, so that the rows constitute an orthonormal basis of V. The columns of the matrix form another orthonormal basis of V.
Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage. [5] More rigorously, if we assume that a test case has parameters given in a set {} = {,,...