Ideal of an inversable triangular matrix

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The discussion revolves around proving that a function f belonging to the ideal of an invertible block matrix P can be expressed as a sum of regular functions g_{ij}. The matrix P is defined as P=[a b; 0 d], and its invertibility is crucial to the argument. Participants seek clarification on the terminology, specifically what constitutes "the ideal of the matrix" and "regular functions above the space of invertible matrices." Understanding these concepts is essential for addressing the proof. The conversation emphasizes the need for a clear definition of terms to facilitate further discussion on the mathematical proof.
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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