On Differentiating a Matrix
- 1 May 1927
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 1 (2) , 111-128
- https://doi.org/10.1017/s0013091500007434
Abstract
The theorem is well known. So also is the theorem that if concerning a determinant Λ and its reciprocal expressed by means of cofactors Aij of aij. Not quite so well known is the Cayley Hamilton theorem that a matrix X =[xij] satisfies its own characteristic equationUnlike as these three results are, they nevertheless can be looked upon as particular phases of a general theorem concerning a matrix differential operator acting upon a function of a matrix X or its transposed.Keywords
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