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A Course In Functional Analysis

A hilbert space problem book

Book dedication.- Preface.- Part I: State-of-the-art surveys & original matrix theory work.- Part II: Advanced matrix theory for radar processing.- Part III: Matrix-based signal processing applications.- Index of terms

Matrix Information Geometry

https://www.isibang.ac.in/~jay/OTOA2014/ctalks/PG.pdf

Characterization of Birkhoff–James orthogonality

https://www.opt.mist.i.u-tokyo.ac.jp/~nakatsukasa/publishedpdf/pub15.pdf

The minimization of matrix logarithms: On a fundamental property of the unitary polar factor

https://www.isid.ac.in/~statmath/2012/isid201207.pdf

Norm inequalities related to the matrix geometric mean

https://www.isid.ac.in/~statmath/2013/isid201315.pdf

Orthogonality to matrix subspaces, and a distance formula

We obtain necessary and sufficient conditions for a matrix A to be Birkhoff-James orthogonal to another matrix B in the Ky Fan k-norms. A characterization for A to be Birkhoff-James orthogonal to any subspace of is also obtained.

Orthogonality of matrices in the Ky Fan k-norms

The norm of the mth derivative of the map that takes an operator to its kth antisymmetric tensor power is evaluated. The case m = 1 has been studied earlier by Bhatia and Friedland (R. Bhatia and S. Friedland. Variation of Grassman powers and spectra. Linear Algebra and its Applications, 40:1-18, 1981). For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown that a positive m-linear map between C � -algebras attains its norm at the m-tuple (I, I,...,I). Expressions for derivatives of the maps that take an operator to its kth tensor power and kth symmetric tensor power are also obtained. The norms of these derivatives are computed. Derivatives of the map taking a matrix to its permanent are also evaluated.

/pdf/derivatives-of-tensor-powers-and-their-norms-392x1xr6na.pdf

Priyanka Grover

Papers

Characterization of Birkhoff–James orthogonality

Norm inequalities related to the matrix geometric mean

Orthogonality to matrix subspaces, and a distance formula

Orthogonality of matrices in the Ky Fan k-norms

Derivatives of tensor powers and their norms