Skip to content

Hessenberg Transformation Beispiel Essay

1. Introduction

Let denote the space of all n-square matrices over the complex field and let be the symmetric group of degree n. For , the permanent function is defined as:
The permanent function therefore resembles the determinant, which in turn is given by: where denotes the sign function.
Although not as prominent as the determinant, the permanent function is still a well-known matrix function, with many applications in combinatorics and graph theory. However, while the determinant can be easily computed, no efficient algorithm for computing the permanent is known. The difficulty for a direct computation of the permanent leads to the idea of trying to compute it by using determinants. This problem dates back to 1913 in a work by Pólya [1], and it has been under intensive investigation since then. While it is clear that the permanent of a matrix: equals the determinant of the related matrix:

Szegö [2] proved that for , there is no way to generalize this procedure. That is, there is no uniform way of changing the signs in the entries of a matrix in order to obtain a matrix B satisfying .

In [3], Gibson proved that if A is an n-square -matrix, and if the permanent of A can be converted to a determinant by affixing ± signs to the elements of the matrix, then A has at most positive entries.

Later, Little [4] proved that an n-square -matrix can be conveniently represented by means of a bipartite graph and reinterpreted the problem of characterizing convertible matrices as the problem of characterizing bipartite graphs whose 1-factors can be counted by using Pfaffians in the manner suggested by Kasteleyn [5].

The computational complexity for determining if a -matrix is convertible was studied by Vazirani and Yannakakis [6] and Robertson, Seymour, and Thomas [7], leading the latter authors to design a polynomial-time algorithm capable of determining whether or not the permanent of the matrix is convertible into a determinant.

In this article, we consider mostly n-square -matrices with the maximum number of positive entries . For these cases, we present a procedure to determine whether or not a given matrix is convertible. Compared with previously available algorithms, this method does not rely on the associated bipartite graph, and is more efficient. This result is presented in Section 4, where we introduce a new concept: the imprint. Before that, in Section 3, we define Hessenberg-type matrices, generalizing the well-known notion of Hessenberg matrices, and present some preliminary results. Our main results are presented in Section 5. We extend Fonseca’s result [8] by presenting an explicit characterization of convertible Hessenberg-type matrices and corresponding subspaces. We conclude that convertible matrices can be reduced to a basic set.

2. Basic Definitions and Preliminary Results

Let us start with a brief summary of definitions and results that are subsequently used throughout the article.

In the present work, we exclusively consider square matrices, so we will drop the qualifier square in what follows. In general, the order n of the considered matrices is arbitrary, except when explicitly stated otherwise.

A matrix is said to be convertible if there exists a -matrix , such that: where ★ denotes the Hadamard product. As already mentioned in the Introduction, a convertible matrix of order n has at most nonzero entries [3].
For a -matrix S of order n, we define the associated coordinate subspace as:
It is clear that if S is convertible then every element of is also convertible, with respect to the same matrix C; i.e., there exists a -matrix such that:

We will also say that is convertible.

Do you need help with with essay, research paper, homework or even dissertation?

Visit our website — https://goo.gl/HKbmHS (assignmenthelp24.com)

=================>>>CLICK HERE<<<=================

=================>>>CLICK HERE<<<=================

=================>>>CLICK HERE<<<=================

=================>>>GET ASSIGNMENT HELP<<<=================

=================>>>GET ASSIGNMENT HELP<<<=================

=================>>>GET ASSIGNMENT HELP<<<=================

hela zellen dissertation definition

la litterature africaine dissertation

journal of college admission essay contest

nuage lenticulaire explication essay

are short essays underlined or italicized

discipline poem analysis essays

what is a good cover letter font

avengers 2 age of ultron analysis essay

1000 word essay being on time

the road by mccarthy essay

analyzing essay

innuitian region descriptive essay

writing a descriptive essay on a place

us spending on healthcare research paper

color kinetics incorporated case study analysis format

malcolm x and mlk compare contrast essay

volvo case study pdf format

culture and identity argumentative essay structure

antoine hermary bibliography de mariama ba

civil engineering graduate school personal statement

hero old man and the sea essay

say not the struggle naught availeth essay

eec 11 assignment 2012 toyota

friend and friendship essay of mice

maths assignment title page

industrial psychology essay topics

navy bmr assignment 8 flashcards quizlet

band 6 essay shoe horn sonatas

this i believe npr essays

homeworknow shjsu

mcs 032 solved assignment 2014-15

hrm 300 week 1 essays on abortion

alternative fuels for automobiles research paper

world checklist and bibliography of euphorbiaceae columnar

simple basic cover letter for employment

how to introduce a short story in an essay

thesis statement for cause and effect of ww1

essay writing service article

a monk’s tale cultural values essay

essay on trade fair in bangladesh what do pumpkins

personal statement guide cvx

essay linking words ielts exam

argumentative essay on fast food pro and con

fur trade in new france essay

discovering myself essays

the eagleman stag essay writer

neodymium laser transitions for essays

post literacy definition essay

interesting or amusing story about yourself essayscorer

dictionary skills assignment

essays over salem witch trials

synthesis and response essay

thesis and dissertation topics

corrig dissertation bac franais 2004

kendriya vidyalaya tirumalagiri homework answers

moulsham high school show my homework

istanbul hakkinda essay

essay value computer education today in the Where Can I Find Someone to Write My College Paper united

review essay on adhd websites

titles for water pollution essays

islamic banking dissertation pdf writer

essayiste rap

the road not taken photo essay pictures

sample student case study analysis

religious tolerance essays

4 functions of management case study

alexander pope an essay on criticism audio-technica

chronological order essay examples

illustration essay on eating disorders

the awakening bird symbolism essay

rappaccini’s daughter symbolism essay ideas

code of federal regulations title 41 section 102-79 assignment and utilization of space

satisfactory moral theory essays on love

end essay conclusion

cons globalization essay against globalization

wenchuan earthquake essay with headings

internet essay in hindi pdf

my best friend essay quotes from lord

peer pressure alcohol essay topics

the lead of a process essay is designed to do

fpv goggles comparison essay

boss battle music extended essay

essay friendship 250 words to describe

does bibliography or works cited come first of may song

character analysis essay for beowulf

almaghrib scholarship essay

conclusion essay racism in america

critical thinking skills activities

bibliography of data related literature of absenteeism

hamlet and the great gatsby comparison essay

free research paper on adhd

cover letters for teachers seeking employment

around the world in 80 days essay

structure collapse case study

rescriptor classification essay

chicago style bibliography primary and secondary sources game

write gcse english poetry essay

zfs checksum algorithm comparison Where Can I Find Someone to Write My College Paper essay

what is the best custom essay service reviews

tiepoint analysis essay

got a 4 on sat essay writing

preparing an Where Can I Find Someone to Write My College Paper essay outline

bb0031 assignment of rents

selfie discursive essay ppt

ana synthesis essay

father essay titles

essay on the equality of human races

oxford happiness questionnaire descriptive essay

a five paragraph essay on black mamba

off site manufacturing dissertation examples

perhaps the world ends here essay

marriotts school show my homework

bodley head/ft essay prize 2014 nfl

new state academy holiday homework cover

third hand smoking research paper

importance of our culture essay anthropology

free always running essay

biol 5 essay atp

eco technology essay writing

caribbean studies cape essays on success

multiculturalism in canada thesis statement

atomic energy central school 2 hyderabad admissions essay

how do Where Can I Find Someone to Write My College Paper write a critical reflection essay

dissertation zitieren hausarbeiterin

essay extended

professional business cover letters

essay for 10th class with quotations Where Can I Find Someone to Write My College Paper about family

assignment 4 merger acquisition and international strategies of mcdonalds

coastal soft engineering case study

us general accounting office case study evaluations hrc

critical thinking alec fisher ebook

homework hawk level c review units 1-3 analogies

how to write reflection essay

colorscope case study analysis format

houghton mifflin math grade 1 homework pages

craniata eggs classification essay

talentlens critical thinking test questions

how to format dialogue into an essay

second great awakening reform movements essay writer

ask librarian homework help

ethnographic research papers

Where Can I Find Someone to Write My College Paper northwestern law school application essays

writing research paper video

short essay on patriotism in pakistan

manage pgdaem assignment submission

happy and prosperous nation india essays

indian school wadi kabir holiday homework class

orchard technology essay scholarship oppurtunity

blog homework help

broward schools reassignment office