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Some compiled languages such as Ada and Fortran, and some scripting languages such as IDL, MATLAB, and S-Lang, have native support for vectorized operations on arrays. For example, to perform an element by element sum of two arrays, a and b to produce a third c , it is only necessary to write
Statement separator – demarcates the boundary between two statements; need needed for the last statement; Line continuation – escapes a newline to continue a statement on the next line; Some languages define a special character as a terminator while some, called line-oriented, rely on the newline.
The Computer Language Benchmarks Game site warns against over-generalizing from benchmark data, but contains a large number of micro-benchmarks of reader-contributed code snippets, with an interface that generates various charts and tables comparing specific programming languages and types of tests. [56]
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
R-diagrams can be used to easily simplify complicated logical expressions, using a step-by-step process. Using order of operations, logical operators are applied to R-diagrams in the proper sequence. Finally, the result is an R-diagram that can be converted back into a simpler logical expression. For example, take the following expression:
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true. The truth table of p EQ q (also written as p = q, p ↔ q, Epq, p ≡ q, or p == q) is as follows: The Venn diagram of A EQ B (red part is true)
Compare with unitary matrices. Congruent matrix: Two matrices A and B are congruent if there exists an invertible matrix P such that P T A P = B. Compare with similar matrices. EP matrix or Range-Hermitian matrix A square matrix that commutes with its Moore–Penrose inverse: AA + = A + A. Idempotent matrix or Projection Matrix