XII.—Studies in Practical Mathematics. I. The Evaluation, with Applications, of a Certain Triple Product Matrix
XII.—Studies in Practical Mathematics. I. The Evaluation, with Applications, of a Certain Triple Product Matrix
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XII.—实用数学研究 I. 某个三重乘积矩阵的评估及其应用
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发表时间：
1938
期刊：
影响因子：
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通讯作者：
A. C. Aitken
中科院分区：
文献类型：
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作者：
A. C. Aitken
联立线性代数方程组的求解、给定方阵的自共轭或倒数的求值、给定形式的双线性或二次形式的倒数的求值，都是某种一般运算的特殊情况，即矩阵乘积H ′ A-1 K的求值，其中A是平方的且非奇异的，即行列式|一|不是零。（矩阵乘法类似于行列式乘法，但仅限于行到列。矩阵H ′由H通过转置得到，也就是说，通过将行变为列。）矩阵H '和K可以是矩形的。如果A是单数，则倒数A-1不存在;在这种情况下，可能需要乘积H ′（adj A）K。在算术上，计算H ′ A-1 K和H（adj A）K的唯一区别是，在后一种情况下，所有元素的最后除以|一|不执行。
The solution of simultaneous linear algebraic equations, the evaluation of the adjugate or the reciprocal of a given square matrix, and the evaluation of the bilinear or quadratic form reciprocal to a given form, are all special cases of a certain general operation, namely the evaluation of a matrix product H ′ A -1 K , where A is square and non-singular, that is, the determinant | A | is not zero. (Matrix multiplication is like determinant multiplication, but exclusively row-into-column. The matrix H ′ is obtained from H by transposition, that is, by changing rows into columns.) The matrices H ′ and K may be rectangular. If A is singular, the reciprocal A -1 does not exist; and in such a case the product H ′(adj A ) K may be required. Arithmetically, the only difference in the computation of H ′ A -1 K and H (adj A ) K is that in the latter case a final division of all elements by | A | is not performed.