projection from linear subspace algebraic geometry

Applications of CS decomposition in linear combinations of two orthogonal projectors. A short proof of a matrix decomposition with applications. Puntanen (eds), Springer, India, 2013, pp. In: Combinatorial Matrix Theory and Generalized Inverses of Matrices, R.

On the entries of orthogonal projection matrices. Rank formulae from the perspective of orthogonal projectors. Functions of orthogonal projectors involving the Moore–Penrose inverse. On a subspace metric based on matrix rank. On angles and distances between subspaces. Eigenvalues of functions of orthogonal projectors. Revisitation of the product of two orthogonal projectors.

Column space equalities for orthogonal projectors. An alternative approach to characterize the commutativity of orthogonal projectors. Characterizations of EP, normal, Hermitian matrices. Rees ed.), Marcel Dekker, New York, 1993, pp. In Graphs, Matrices, and Designs: Festschrift in Honor of N.J.

Around a formula for the rank of a matrix product with some statistical applications. Generalizations of a property of orthogonal projectors. Puntanen eds.), University of Tampere, Tampere, Finland, 1987, pp. In: Proceedings of the Second International Tampere Conference in Statistics (T. Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. On pairs of projections in a Hilbert space. Orthogonal and oblique projectors and the characteristics of pairs of vector spaces. On the latent vectors and characteristic values of products of pairs of symmetric idempotents. As applications, we give matrix representation for the orthogonal projectors onto the intersections of a pair of linear subspaces using various matrix decomposition identities and Moore–Penrose inverses necessary and su˚cient conditions for two linear subspaces to be in generic position characterization of the commutativity of a pair of orthogonal projectors necessary and su˚cient conditions for equalities and inequalities for a pair of subspaces to hold equalities and inequalities for norms of a pair of orthogonal projectors and their operations as well as a collection of characterizations of EP-matrix. We shall establish a variety of closed-form formulas for representing the direct sum decompositions of the m-dimensional complex column vector space 𝔺 m with respect to a pair of given linear subspaces 𝒨 and 𝒩 and their operations, and use them to derive a huge amount of decomposition identities for matrix expressions composed by a pair of orthogonal projectors onto the linear subspaces.

The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their orthogonal complements in the finite-dimensional complex vector space. Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra.

Projection from linear subspace algebraic geometry