With the assumption that the covariance matrix O is invertible
, the vector of the expected excess rate of return R-r in CAPM can be rewritten as
Since not all multivectors are invertible
, we have to be satisfied with reverses  of multivectors.
Since the latter are assumed to be invertible
, Hilbert-Schmidt norm approximation does not apply.
In particular, if the matrix E is invertible
, then it may be possible to estimate the true sample proportions by multiplying both sides of Equation A3 by the inverse matrix [E.
Moreover, there exists an invertible
matrix A = ([A.
The projective transformation is an invertible
transformation between two projective planes and their essential feature is the point-to-line mapping.
The Western-style semi-buckhorn rear sight has a separate, invertible
notch-plate, giving you a choice of a deep U-notch or a smaller V-notch.
Theorem 6 (Banach Lemma on Invertible
Operators), Argyros (2005):
The algorithm is called invertible
if an attacker creates a faked watermark [W.
The mathematical rationale of the described methods rests on the solvability and inertia of Hermitian solutions of matrix equations, as well as the theory of linear equations with positively invertible
operators in a partially ordered space.
Since we do not assume that A is invertible
, we write
To overcome any potential flow problems with the batch handling of this material, invertible
IBC bins with a larger outlet were used to upset the consolidation of the material and ensure reliable flow.