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...
=∑1⩽i<j⩽n(aibj−ajbi)(cidj−cjdi) 正好得到结论. 另外,当 ai=ci,bj=dj 时,原恒等式即为拉格朗日恒等式(Lagrange's identity),并且由拉格朗日恒等式可以直接得出Cauchy-Schwarz 不等式. 参考 ^minor.Wikipedia ^蓝以中.高等代数简明教程.北京大学出版社.2007 ^Cauchy–Binet formula.Wikipedia ...
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...
Binet2Cauchy )设A是n×m矩阵,B是m×n矩阵,则 AB = 0,当m ∑ (j) A 12…n j1j2…jn B j1j2…jn 12…n ,当m>n. (1) 证 因为 EnAn×m Om×nEm An×mOn×n -EmBm×n = On×m(AB)n×n -EmBm×n , 两边取行列式,得 An×mOn×n ...
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...
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) ...
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]...