Ideal of an inversable triangular matrix

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The discussion centers on the concept of an ideal in the context of an invertible block matrix P=[a b; 0 d]. The user seeks to prove that if a function f belongs to the ideal of the matrix, then it can be expressed as f = ∑g_{ij}x_{ij}, where g_{ij} are regular functions defined over the space of invertible matrices. The inquiry highlights the need for clarity on specific terms such as "ideal of the matrix" and "regular functions" within this mathematical framework.

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karin
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Hello
I need your help please.
I have a block matrix P=[a b ; 0 d], which is inversable.
if f belongs to the ideal of the matrix, how do I prove that
f=\sumg_{ij}x_{ij}
while g_{ij} are regular functions above the space of inversable matrix?
thank you!
Karin
 
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I think you should explain the terminology here. What is "the ideal of the matrix", and what are "regular functions above the space of inversable matrix"?
 

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