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In the [[mathematical]] field of [[linear algebra]], an '''arrowhead matrix''' is a square [[matrix (mathematics)|matrix]] containing zeros in all entries except for the first row, first column, and main diagonal.<ref>{{cite book |author=Stewart, G. W. |title=Matrix Algorithms |publisher=Society for Industrial and Applied Mathematics |location=Philadelphia |year=1998 |pages=204 |isbn=0-89871-503-2}}</ref><ref>{{cite arXiv |eprint=1302.7203 |author1=Nevena Jakovcevic Stor |author2=Ivan Slapnicar |last3=Barlow |first3=Jesse L. |title=Accurate eigenvalue decomposition of arrowhead matrices and applications |class=math.NA |year=2013}}</ref> In other words, the matrix has the form
:<math>\begin{pmatrix}
\,\! *&*&*&*&* \\
\,\! *&*&0&0&0 \\
\,\! *&0&*&0&0 \\
\,\! *&0&0&*&0 \\
\,\! *&0&0&0&*
\end{pmatrix}.</math>
 
Arrowhead matrices are used in some algorithms for finding of [[eigenvalue]]s and [[eigenvector]]s.<ref>{{cite journal|doi=10.1137/S0895479892241287|title=A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem|year=1995|last1=Gu|first1=Ming|last2=Eisenstat|first2=Stanley C.|journal=SIAM Journal on Matrix Analysis and Applications|volume=16|pages=172}}</ref>
 
== References ==
{{Reflist}}
 
[[Category:Matrices]]
 
 
{{Linear-algebra-stub}}

Revision as of 11:43, 5 March 2013

In the mathematical field of linear algebra, an arrowhead matrix is a square matrix containing zeros in all entries except for the first row, first column, and main diagonal.[1][2] In other words, the matrix has the form

(*******000*0*00*00*0*000*).

Arrowhead matrices are used in some algorithms for finding of eigenvalues and eigenvectors.[3]

References

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Template:Linear-algebra-stub

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  2. Template:Cite arXiv
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