2012, 2(2): 293-299. doi: 10.3934/naco.2012.2.293

How to transform matrices $U_1, \ldots, U_p$ to matrices $V_1, \ldots, V_p$ so that $V_i V_j^T= {\mathbb O} $ if $ i \neq j $?

1. 

School of Computer Science, Engineering and Mathematics, Flinders University, Bedford Park, SA 5042, Australia

2. 

School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia

Received  September 2011 Revised  April 2012 Published  May 2012

Methods of a transformation of matrices $U_1, \ldots, U_p$ to matrices $V_1, \ldots, V_p$ are proposed so that $V_i V_j^T={\mathbb O} $ for $ i\neq j $ and $i,j =1,\ldots,p $. We consider unconstrained and constrained problems associated with such a transformation. Solutions of the both problems are provided.
Citation: Vladimir Ejov, Anatoli Torokhti. How to transform matrices $U_1, \ldots, U_p$ to matrices $V_1, \ldots, V_p$ so that $V_i V_j^T= {\mathbb O} $ if $ i \neq j $?. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 293-299. doi: 10.3934/naco.2012.2.293
References:
[1]

T. L. Boullion and P. L. Odell, "Generized Inverse Matrices," John Willey & Sons, Inc., New York, 1972.

[2]

S. Friedland, A. Niknejad and L. Chihara, A simultaneous reconstruction of missing data in DNA microarrays, Linear Alg. Appl., 416 (2006), 8-28. doi: 10.1016/j.laa.2005.05.009.

[3]

J. Listgarten, C. Kadie, E. Schadt and D. Heckerman, Correction for hidden confounders in the genetic analysis of gene expression, Proc. Natl. Acad. Sci. USA, 107 (2010), 16465-16470. doi: 10.1073/pnas.1002425107.

[4]

A. Torokhti and P. Howlett, "Computational Methods for Modelling of Nonlinear Systems," Elsevier, 2007.

[5]

A. Torokhti and P. Howlett, Optimal transform formed by a combination of nonlinear operators: The case of data dimensionality reduction, IEEE Trans. on Signal Processing, 54 (2006), 1431-1444. doi: 10.1109/TSP.2006.870560.

show all references

References:
[1]

T. L. Boullion and P. L. Odell, "Generized Inverse Matrices," John Willey & Sons, Inc., New York, 1972.

[2]

S. Friedland, A. Niknejad and L. Chihara, A simultaneous reconstruction of missing data in DNA microarrays, Linear Alg. Appl., 416 (2006), 8-28. doi: 10.1016/j.laa.2005.05.009.

[3]

J. Listgarten, C. Kadie, E. Schadt and D. Heckerman, Correction for hidden confounders in the genetic analysis of gene expression, Proc. Natl. Acad. Sci. USA, 107 (2010), 16465-16470. doi: 10.1073/pnas.1002425107.

[4]

A. Torokhti and P. Howlett, "Computational Methods for Modelling of Nonlinear Systems," Elsevier, 2007.

[5]

A. Torokhti and P. Howlett, Optimal transform formed by a combination of nonlinear operators: The case of data dimensionality reduction, IEEE Trans. on Signal Processing, 54 (2006), 1431-1444. doi: 10.1109/TSP.2006.870560.

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