The discussion revolves around finding the inverse of a linear operator, denoted as A, under the condition that A² - A + I = 0. Participants are exploring the implications of this equation and the concept of an inverse operator.
Participants are actively engaging with the definitions and properties of the inverse operator. Some guidance has been offered regarding the relationship between A and its inverse, but there is no explicit consensus on the correctness of the proposed expression for A^-1. The conversation reflects a mix of interpretations and reasoning about the problem.
There is a lack of clarity regarding the original operator A and its properties, as well as the absence of a matrix representation, which may affect the discussion. Participants are navigating these constraints while attempting to derive the inverse.
?? No, A-1 doesn't mean anything like that: it means the linear operation that "undoes" A. A-1Ax= x and AA-1x= x.transgalactic said:it means that if we take the image of a certain basis
and put it into the A^-1 we get the original basis
My point was that A(I- A)= I shows that I -A does exactly what we want of the inverse: AA-1= I. Since A(I-A)= I, (and inverses are unique), A-1= I- A.how its going to help me??
thought of certain solution of making some basic multiplication
operations
i got the resolt
A^-1=I-A
is it ok??