Search results
Results from the WOW.Com Content Network
Thus, an matrix of complex numbers could be well represented by a matrix of real numbers. The conjugate transpose, therefore, arises very naturally as the result of simply transposing such a matrix—when viewed back again as an n × m {\displaystyle n\times m} matrix made up of complex numbers.
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in ...
The matrix vectorization operation can be written in terms of a linear sum. Let X be an m × n matrix that we want to vectorize, and let e i be the i -th canonical basis vector for the n -dimensional space, that is e i = [ 0 , … , 0 , 1 , 0 , … , 0 ] T {\textstyle \mathbf {e} _{i}=\left[0,\dots ,0,1,0,\dots ,0\right]^{\mathrm {T} }} .
FlexPro is a commercial program for interactive and automated analysis and presentation of mainly measurement data. It supports many binary instrument data formats and has its own vectorized programming language. IGOR Pro, a software package with emphasis on time series, image analysis, and curve fitting. It comes with its own programming ...
It contains a matrix language, a graphical notebook style interface, and a plot window. Euler is designed for higher level math such as calculus , optimization , and statistics . The software can handle real , complex and interval numbers, vectors and matrices , it can produce 2D / 3D plots , and uses Maxima for symbolic operations.
In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U −1 equals its conjugate transpose U *, that is, if = =, where I is the identity matrix.. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger ( † ), so the equation above is written