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Let $M_{n}$ be the multiplicative semigroup of all $n \times n$ complex matrices, and let $U_{n}$ and $G L_{n}$ be the $n$ –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from $U_{n}$ to $G L_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ , and thereby determine multiplicative homomorphisms from $U_{n}$ to $M_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ . This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if $f : U_{n} \to M_{n}$ is a spectrum–preserving multiplicative homomorphism, then there exists a matrix $R$ in $G L_{n}$ such that $f (A) = R A R$ for...

How tight is Hadamard's bound?

Abbott, John, Mulders, Thom (2001)

Experimental Mathematics

How to characterize commutativity equalities for Drazin inverses of matrices

Yong Ge Tian (2003)

Archivum Mathematicum

Necessary and sufficient conditions are presented for the commutativity equalities $A^{*} A^{D} = A^{D} A^{*}$ , $A^{†} A^{D} = A^{D} A^{†}$ , $A^{†} A A^{D} = A^{D} A A^{†}$ , $A A^{D} A^{*} = A^{*} A^{D} A$ and so on to hold by using rank equalities of matrices. Some related topics are also examined.

How to establish universal block-matrix factorizations.

Tian, Yongge, Styan, George P.H. (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Hurwitz analysis: basic concepts and connection with Clifford analysis

Enrique Ramírez de Arellano, Nikolai Vasilevski, Michael Shapiro (1996)

Banach Center Publications

Hurwitz pairs and Clifford valued inner products

Jan Cnops (1996)

Banach Center Publications

After an overview of Hurwitz pairs we are showing how to actually construct them and discussing whether, for a given representation, all Hurwitz pairs of the same type are equivalent. Finally modules over a Clifford algebra are considered with compatible inner products; the results being then aplied to Hurwitz pairs.

Hybrid Algorithm for Fast Toeplitz Orthogonalization.

Sanzheng Qiao (1988)

Numerische Mathematik

Hypercomplex Algebras and Geometry of Spaces with Fundamental Formof an Arbitrary Order

Mikhail P. Burlakov, Igor M. Burlakov, Marek Jukl (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

In this paper a complete characterization of hyperreflexive operators on finite dimensional Hilbert spaces is given.

Hypersymmetric functions and Pochhammers of $2 \times 2$ nonautonomous matrices.

Antippa, A.F. (2004)

International Journal of Mathematics and Mathematical Sciences

Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products.

Mehl, Christian, Ran, André C.M., Rodman, Leiba (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Higher-order linear matrix descriptor differential equations of Apostol-Kolodner type.

High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.

Hintereinanderausführung von Formen.

H-normal matrices

Hochschild cohomology and deformations of Clifford-Weyl algebras.

Homomorphisms for Distributive Operations in Partial Algebras. Applications to Linear Operators and Measure Theory.

Homomorphisms from the unitary group to the general linear group over complex number field and applications