We could use matrix multiplication on these to generate a 3x3 matrix. // 列向量乘以行向量得到一个矩阵 Transpose[{vec}].{vec} {{1, 2, 3}, {2, 4, 6}, {3, 6, 9}} 1. 2. 3. Or obtain the dot product, in a rather silly way, as a 1x1 matrix. // 行向量乘以列向量得到一个...
Not Symbols 2.2.9 Advanced Topic: Working with Operators 2.2.10 Structural Operations 2.2.11 Sequences Patterns 2.3.1 Introduction 2.3.2 Finding Expressions That Match a Pattern 2.3.3 Naming Pieces of Patterns 2.3.4 Specifying Types of Expression in Patterns 2.3.5 Putting Constraints on Patterns ...
There was something similar with recursion control. I thought it was bad to havef[$x] : $x f[$x-1](with no end condition forf[1]) go into an infinite loop trying to evaluatef[-1],f[-2], etc. Because after all, at some point there’s multiplication by 0. So why not just ...
16.15 Matrix Representation of the Linear Operator 359 17 Application of Mathematica to Quantum Mechanics 361 17.1 Introduction 361 17.2 A Particle in a One-Dimensional Box 361 17.3 A Particle in a Two-Dimensional Box 365 17.4 The Hydrogen Atom Problem 368 ...
We’ve been working towards it for nearly 15 years… but finally it’s here: computation with video! We introduced images into the language in 2008; audio in 2016. But now in Version 12.1 we for the first time have computation with video. There’ll be lots more co...
It’s just “free” inside your program to solve a traveling salesman problem, or to do elaborate image processing, or to diagonalize a giant sparse matrix.And all this stuff is completely integrated in a coherent way into the core system. You’re not chasing libraries, buying random tool...
The declaration of domain of the symbol is not necessary if a value was assigned to the symbol, e.g., if x = c * v1, the symbol v must be Vector, c must be Scalar and x can be undeclared. à Vectors and polynomials. The multiplication The vectors in SuperLie look like the ...
The Matrix object has 2 properties r and i for respectively real and imaginary parts of matrix elements. These are the actual aforementioned JS TypedArrays. The imaginary property part is optional if it is not defined the Matrix represents solely an array of real elements. Details (click to sh...
Each f_i - f_1 is, up to multiplication by -1, an element of S_{dec}(\Gamma ). Thus f lies in (g)_{g \in S_{dec}(\Gamma )}. It follows that elements of S_{dec}(\Gamma ) generate the ideal I_{dec}(\Gamma ). \square Applying Proposition 2.17, we can conclude that...