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In particular, the direct sum of square matrices is a block diagonal matrix. The adjacency matrix of the union of disjoint graphs (or multigraphs) is the direct sum of their adjacency matrices. Any element in the direct sum of two vector spaces of matrices can be represented as a direct sum of two matrices. In general, the direct sum of n ...
(A \ A)* x ==A \ b (associativity also holds for matrices, commutativity is no more required) x = A \ b This is not only an example of terse array programming from the coding point of view but also from the computational efficiency perspective, which in several array programming languages benefits from quite efficient linear algebra libraries ...
Comparison of Java and .NET platforms ALGOL 58's influence on ALGOL 60; ALGOL 60: Comparisons with other languages; Comparison of ALGOL 68 and C++; ALGOL 68: Comparisons with other languages; Compatibility of C and C++; Comparison of Pascal and Borland Delphi; Comparison of Object Pascal and C; Comparison of Pascal and C; Comparison of Java and C++
Java: 2006 Yes 3D Cross-platform: GPL: Java port of Quake II game engine Java 3D: Java: Yes 3D Cross-platform: BSD: Community-centric project. Used by many schools as part of course work Jedi: C: Yes 2.5D DOS, Windows: Star Wars: Dark Forces, Outlaws: Proprietary: Rumored to have been reverse-engineered from Doom engine jMonkeyEngine: Java ...
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
Examples include the vector space of -by-matrices, with [,] =, the commutator of two matrices, and , endowed with the cross product. The tensor algebra T ( V ) {\displaystyle \operatorname {T} (V)} is a formal way of adding products to any vector space V {\displaystyle V} to obtain an algebra. [ 88 ]
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .