![]() The first step is to identify is the matrix is square or not.Following are the steps to identify the diagonal matrix: The same, as occurs, for example, if for some positive integer n,Īll the matrices start as mat or mat. The algebra of additions and multiplications involving both one-Īnd two-dimensional matrices is particularly simple when all theĮlements are real or complex numbers and all the index-lists are Multiplied on the right by the corresponding element of B. Result has the same index-lists as A each column of A is If number of columns in A is the same as the size of A. If A is of dimension 2 and B is of dimension 1, A * B is defined On the left by the corresponding element of A. Result has the same index-lists as B each row of B is multiplied ![]() If the number of rows in B is the same as the size of A. ![]() If A is of dimension 1 and B is of dimension 2, A * B is defined Taken to represent 2D matrices for which the off-diagonal elementsĪre zero and the diagonal elements are those of A and B. Is consistent with multiplication of 2D matrices if A and B are If A and B have the same index-list, this multiplication Have the same size the result has the same index-list as AĪnd each element is the product of corresponding elements ofĪ and B. If both A and B have dimension 1, A * B is defined if A and B That of multiplying the elements of the other matrix on the If A or B has dimension zero, the result for A * B is simply If the multiplications and additions required cannot be performed,Īn execution error may occur or the result for C may contain The sameįormula is used so long as the number of columns in A is the sameĪs the number of rows in B and k is taken to refer to the offsetįrom matmin(A,2) and matmin(B,1), respectively, for A and B. The sum being over k in the column-index-list of A. Way so that for i in the row-index-list of A and j in theĬolumn-index-list for B, C = Sum A * B The row-index-list for B, C = A * B is defined in the usual If both haveĭimension 2 and the column-index-list for A is the same as Multiplication is defined provided certain conditions by theĭimensions and shapes of A and B are satisfied. (Both are available on Linux/OSX/Windows) CalcĮxample matrix assignment: mat = ĭocumentation for multiplication of matrices: It has a command-line mode, as well as a web notebook interface (as an example, a public server run by the main developers).Īnd, although this might not be relevant since your use-case sounds very simple, the syntax is just Python with a small preprocessing step to facilitate some technical details and allow some extra notation (like which expands to ), so many people already know it and, if not, learning it is very easy.Īs a slight tangent, Sage is actually the origin of the increasingly popular Cython language for writing fast "Python", and even offers an easy and transparent method of using Cython for sections of code in the notebook.ĭepending on my use-case I either use Calc the C-style arbitrary precision calculator or bc. It includes GP/Pari and maxima, and so does symbolic manipulations and number theory at least as well as them. There are many algorithms implemented as a direct part of Sage, as well as wrapping many other open-source mathematics packages, all into a single interface (the user never has to tell which package or algorithm to use for a given computation: it makes the decisions itself). Sage is basically a Python program/interpreter that aims to be an open-source mathematical suite (ala Mathematica and Magma etc.).
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