A Generalized Matrix Inverse That Is Consistent with Respect to Diagonal Transformations

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space ...

[1]  Richard Sinkhorn,et al.  Concerning nonnegative matrices and doubly stochastic matrices , 1967 .

[2]  Uriel G. Rothblum,et al.  Scalings of matrices satisfying line-product constraints and generalizations , 1992 .

[3]  Joseph Duffy,et al.  The fallacy of modern hybrid control theory that is based on "orthogonal complements" of twist and wrench spaces , 1990, J. Field Robotics.

[4]  Zi-Quan Hong,et al.  Algebraic feature extraction of image for recognition , 1991, Pattern Recognit..

[5]  Kei Takeuchi,et al.  Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition , 2011 .

[6]  Jeffrey Uhlmann.  Unit Consistency, Generalized Inverses, and Effective System Design Methods , 2016, ArXiv.

[7]  K..  Dynamic Map Building and Localization : New Theoretical Foundations , 2015 .

[8]  R. Michelena.  Singular value decomposition for cross-well tomography , 1993 .

[9]  Stephen L. Campbell,et al.  Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients , 1976 .

[10]  James G. Berryman,et al.  Analysis of Approximate Inverses in Tomography I. Resolution Analysis of Common Inverses , 2000 .

[11]  M. Drazin.  Pseudo-Inverses in Associative Rings and Semigroups , 1958 .

[12]  Gregory J. Meyer.  Classification of Radar Targets Using Invariant Features , 2012 .

[13]  Tieniu Tan,et al.  Do singular values contain adequate information for face recognition? , 2003, Pattern Recognit..

[14]  Keith L. Doty,et al.  A Theory of Generalized Inverses Applied to Robotics , 1993, Int. J. Robotics Res..

[15]  Chaur-Chin Chen,et al.  Singular value decomposition for texture analysis , 1994, Optics & Photonics.

[16]  Richard Sinkhorn.  A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices , 1964 .

[17]  Wee Hyong Tok,et al.  A Framework for Similarity Search of Time Series Cliques with Natural Relations , 2012, IEEE Transactions on Knowledge and Data Engineering.

[18]  D. Botstein,et al.  Singular value decomposition for genome-wide expression data processing and modeling. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Yeong-Ho Ha,et al.  Video Sequence Matching Using Singular Value Decomposition , 2006, ICIAR.

[20]  Gene H Golub,et al.  Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Brian W. Pogue,et al.  Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography , 2010, Biomedical optics express.