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...
cauchy-binet formular 下载积分: 700 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 ...
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...
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...
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...
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]...
In Section 2 we give an account of the ingredients we need, and, in Section 3, we state and prove the main formula (Theorem 1) without determinants and in a more general setup; a corollary of it is the classical Cauchy–Binet formula. Then, in Section 4, we see that the formula ...
摘要: 给出了Binet-Cauchy公式的三个应用:用此公式证明恒等式;用此公式证明不等式;用此公式计算行列式.关键词:Binet-Cauchy公式 应用 恒等式 不等式 行列式 DOI: 10.3969/j.issn.1004-9444.2001.04.003 年份: 2001 收藏 引用 批量引用 报错 分享 全部来源 免费下载 求助全文 国家科技图书文献中心 (权威机构) ...