<abstract xmlns="http://www.w3.org/1999/xhtml"><p>If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2019-0028_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi><mo>=</mo><mrow><mo>(</mo><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext>I</mtext></mrow><mtext>r</mtext></msub></mrow></mtd><mtd><mtext>O</mtext></mtd></mtr><mtr><mtd><mtext>O</mtext></mtd><mtd><mtext>O</mtext></mtd></mtr></mtable></mrow><mo>)</mo></mrow></mrow></math><tex-math>s = \left( {\matrix{  \hfill {{{\rm{I}}_{\rm{r}}}} &amp; \hfill {\rm{O}} \cr  \hfill {\rm{O}} &amp; \hfill {\rm{O}} \cr } } \right)</tex-math></alternatives></inline-formula>. This is the rank normal form of the matrix A.</p><p>The purpose of this paper is to exhibit some consequences of this representation form.</p></abstract>

If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO)s = \left( {\matrix{  \hfill {{{\rm{I}}_{\rm{r}}}} & \hfill {\rm{O}} \cr  \hfill {\rm{O}} & \hfill {\rm{O}} \cr } } \right). This is the rank normal form of the matrix A.The purpose of this paper is to exhibit some consequences of this representation form.

Some consequences of the rank normal form of a matrix

Institute of Mathematical Statistics and Applied Mathematics

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Some consequences of the rank normal form of a matrix"}

If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO)s = \left( {\matrix{  \hfill...

Some consequences of the rank normal form of a matrix

Pubblicato online: 27 feb 2020

Pagine: 380 - 386

Ricevuto: 31 gen 2019

DOI: https://doi.org/10.2478/ausm-2019-0028

Parole chiave
rank of matrices

© 2019 Sorin Rădulescu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Some consequences of the rank normal form of a matrix

Pubblicato online: 27 feb 2020

Pagine: 380 - 386

Ricevuto: 31 gen 2019

DOI: https://doi.org/10.2478/ausm-2019-0028

Parole chiaverank of matrices

© 2019 Sorin Rădulescu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parole chiave
rank of matrices