scholarly journals Green's matrix for a second-order self-adjoint matrix differential operator

2010 ◽  
Vol 43 (12) ◽  
pp. 125205
Author(s):  
Tahsin Çağrı Şişman ◽  
Bayram Tekin
Keyword(s):  
Differential Operator ◽  
Second Order ◽  
Adjoint Matrix ◽  
Matrix Differential Operator ◽  
Green’S Matrix ◽  
Matrix Differential

scholarly journals On Differentiating a Matrix

1928 ◽  
Vol 1 (2) ◽  
pp. 111-128 ◽  
Author(s):  
H. W. Turnbull
Keyword(s):  
Differential Operator ◽  
Characteristic Equation ◽  
General Theorem ◽  
Matrix Differential Operator ◽  
Matrix Differential ◽  
Image Position

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.

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