The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Componentwise and Cartesian decompositions of linear relations”

A Simple Proof of the Polar Decomposition Theorem

Paweł Wójcik (2017)

Annales Mathematicae Silesianae

Similarity:

In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.

The generalized equations of Riccati and their applications to the theory of linear differential equations

T. Iwiński

Similarity:

CONTENTSIntroduction.............................................................................................................................. 31. Definition of the Riccati equation of the n-th order....................................................... 62. Theorems on the existence of solutions of R equations. Relations between the solutions of linear differential equations and the solutions of the corresponding R equations..................................................................................................

On a decomposition for pairs of commuting contractions

Zbigniew Burdak (2007)

Studia Mathematica

Similarity:

A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.

Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2016)

Formalized Mathematics

Similarity:

In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization. ...