Cauchy-Binet Formula Result: -0.024448590606853515 Direct Calculation of det(AB): -0.02444859060685353 【gemini-1.5-pro-api-0514】 Binet-Cauchy 矩阵行列式公式听起来确实有点神秘, 但其实它是一个非常优美且实用的公式,可以用来计算两个矩阵乘积的行列式。 让我来为你揭开它的神秘面纱: 公式真身: 对于两个矩阵...
Cauchy–Binet formula aaaaa 1 人赞同了该文章 设A,B 分别为 n×s 和s×n 矩阵,则有 (1) 当n>s 时, det (AB)=0 (2) 当n=s 时, det (AB)=det(A)⋅det(B) (3) 当n<s 时, det (AB)=∑1≤i1≤i2<⋯<in<sA(12⋯ni1i2⋯in)⋅B(i1i2⋯in12⋯n) 发布...
内容提示: 642:550, Summer 2004, Supplement 3The Cauchy-Binet formulaSummer 20041. Introductionofthedeterminantsofthefactorsissomemorablethatoneislikelytolosesightofthedif cultyofitsproof.One proof uses Gaussian elimination to write a matrix as a product of elementary matrices and exploits thefact that...
Cauchy-BinetMultiparameter quantum deformationThe quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an easy way to...
On the other hand, for the Cauchy-Binet formula, A ψ = (B ψ ) T , so det(A ψ ) = det(B ψ ), and the formula reduces to det(B T B) =ψ det(B ψ ) 2 . (2) This says that the square of the volume is the sum of the squares of the volumes of the projections of...
aThe formula can be generalized to (square) products of rectangular matrices, giving the Cauchy-Binet formula, which also provides an independent proof of the multiplicative property. 惯例可以是长方形矩阵广义(方形的)产品,给Cauchy-Binet惯例,也提供乘物产的独立证明。[translate]...
The 2 by 2 matrix AB = (2 by 3)(3 by 2) has a “Cauchy–Binetformula” for detAB:detAB = sum of (2 by 2 determinants in A) (2 by 2 determinants in B).eg.毕竟老师没教过这个 关于它的资料我也只搜到维基百科的。所以有几个问题想问:1.矩阵A为N by M的话,N必须小于等于M吗?2...
When N⩾n, an inspection of the zN−n coefficient gives the Cauchy–Binet formula (1). On the other hand, the Cauchy–Binet formula is a generalization of the Pythagorean theorem. Indeed, let A be an n×N real matrix, n⩽N, and take B=AT, the transpose of A. Since Bσ=(AT...
decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula... M Vidyasagar,N Viswanadham - 《Systems & Control Letters》 被引量: 22发表: 1983年 ...