For 10 points, name this operation that, for a matrix, returns another matrix that multiplies the first matrix to return the identity matrix.
For a bounded operator on a normed space, this operation on the operator has a solution if the Neumann series converges. Of the three objects in the Iwasawa decomposition, the one designated K has the property that this operation is equal to the transpose of K. The equivalency class of an object in a group is defined by flanking the element with two elements of the group that are related by this operation. The Cayley-Hamilton theorem can be used to compute this operation for a matrix, and the existence of a solution to this operation can be shown by proving that the determinant is nonzero. For 10 points, name this operation that, for a matrix, returns another matrix that multiplies the first matrix to return the identity matrix.
For a bounded operator on a normed space, this operation on the operator has a solution if the Neumann series converges.
finding the inverse [or inverting; or obvious equivalents]