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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).
where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning =) and R is an upper triangular matrix (also called right triangular matrix). If A is invertible, then the factorization is unique if we require the diagonal elements of R to be positive.
In other words, the space of orthonormal bases is like the orthogonal group, but without a choice of base point: given the space of orthonormal bases, there is no natural choice of orthonormal basis, but once one is given one, there is a one-to-one correspondence between bases and the orthogonal group.
The first idea behind the Proper Orthogonal Decomposition (POD), as it was originally formulated in the domain of fluid dynamics to analyze turbulences, is to decompose a random vector field u(x, t) into a set of deterministic spatial functions Φ k (x) modulated by random time coefficients a k (t) so that:
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
An orthogonal instruction set does not impose a limitation that requires a certain instruction to use a specific register [1] so there is little overlapping of instruction functionality. [ 2 ] Orthogonality was considered a major goal for processor designers in the 1970s, and the VAX-11 is often used as the benchmark for this concept.
The first two steps of the Gram–Schmidt process. In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.
A dyadic tensor T is an order-2 tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b. Analogous to vectors, it can be written as a linear combination of the tensor basis e x ⊗ e x ≡ e xx, e x ⊗ e y ≡ e xy, ..., e z ⊗ e z ≡ e zz (the right-hand side of each identity is only an abbreviation ...