Results 1  10
of
394
ON THE FIELD OF VALUES OF OBLIQUE PROJECTIONS ∗
, 2010
"... Abstract. We highlight some properties of the field of values (or numerical range) W (P) of an oblique projector P on a Hilbert space, i.e., of an operator satisfying P 2 = P. If P is neither null nor the identity, we present a direct proof showing that W (P) = W (I − P), i.e., the field of values ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
of an oblique projection coincides with that of its complementary projection. We also show that W (P) is an elliptical disk with foci at 0 and 1 and eccentricity 1/‖P ‖. These two results combined provide a new proof of the identity ‖P ‖ = ‖I−P ‖. We discuss the relation between the minimal canonical angle
Oblique projections and Schur complements
 Acta Sci. Math. (Szeged
"... Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈, 〉A: H × H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ,η〉A = 〈Aξ,η 〉 , ξ, η ∈ H. Given T ∈ L(H), T is Aselfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of Asel ..."
Geometry of oblique projections
 Studia Math
, 1999
"... Let A be a unital C ∗algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps ϕp: P → Pa sending p to the unique q ∈ Pa with ..."
Abstract

Cited by 10 (8 self)
 Add to MetaCart
Let A be a unital C ∗algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps ϕp: P → Pa sending p to the unique q ∈ Pa
Signal Processing Applications of Oblique Projection Operators
 IEEE Transactions on Signal Processing
, 1994
"... Abstruct Oblique projection operators are used to project measurements onto a lowrank subspace along a direction that is oblique to the subspace. They may be used to enhance signals while nulling interferences. In this paper, we give several basic results for oblique projections, including formula ..."
Abstract

Cited by 49 (0 self)
 Add to MetaCart
Abstruct Oblique projection operators are used to project measurements onto a lowrank subspace along a direction that is oblique to the subspace. They may be used to enhance signals while nulling interferences. In this paper, we give several basic results for oblique projections, including
Lipschitz continuity of oblique projections
 Proc. Amer. Math. Soc
, 1999
"... Abstract. Let W and L be complementary spaces of a finite dimensional unitary space V and let P (W, L) denote the projection of V on W parallel to L. Estimates for the norm of P (W, L) − P (W, M) are derived which involve the norm of the restriction of P (W, L) toMor the gap between L and M. 1. Int ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. Let W and L be complementary spaces of a finite dimensional unitary space V and let P (W, L) denote the projection of V on W parallel to L. Estimates for the norm of P (W, L) − P (W, M) are derived which involve the norm of the restriction of P (W, L) toMor the gap between L and M. 1
Geometry of unitary orbits of oblique projections
"... We study those orbits of oblique projections under the action of the full unitary group of a Hilbert spaceH, which are submanifolds of B(H). We also consider orbits under the Schatten unitaries, and obtain a partial characterization of the submanifold condition for these orbits. Finsler metrics are ..."
Abstract
 Add to MetaCart
We study those orbits of oblique projections under the action of the full unitary group of a Hilbert spaceH, which are submanifolds of B(H). We also consider orbits under the Schatten unitaries, and obtain a partial characterization of the submanifold condition for these orbits. Finsler metrics
Iterative algorithms with seminorminduced oblique projections
, 2002
"... A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices
Joint Channel and Symbol Estimation by Oblique Projections
, 2001
"... The problem of simultaneous blind channel and symbol estimation of a singleinput multipleoutput (SIMO) communication channel is considered in this paper. It is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finit ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
the finite sample convergence property. Furthermore, this estimator can be obtained by the use of oblique projections. An order detection algorithm that avoids the use of subjective thresholding is also proposed. Applications to multiuser detection are also considered. Index TermsBlind channel
Results 1  10
of
394