18 citations · 39 across the 11 of their papers we have counts for
13 papers
Properties of best approximations with respect to the Ky Fan - norm, and the strict spectral approximant of a matrix
Priyanka Grover, Krishna Kumar Gupta
Some questions raised in [K. Ziętak, {\it From the strict Chebyshev approximant of a vector to the strict spectral approximant of a matrix}, Warsaw : Banach Center Publ., 112 Polis…
Subdifferential of the norm, and approximate orthogonality
Priyanka Grover, Krishna Kumar Gupta, Susmita Seal
We present an expression for the right hand derivative of the norm generalizing the result for in [D. J. Keki$\grav…
Inertia and other properties of the matrix
Priyanka Grover, Veer Singh Panwar
Let , and , respectively, denote the number of positive, zero and negative eigenvalues of the matrix . Then the triplet is called the \em…
Bidiagonal decompositions and total positivity of some special matrices
Priyanka Grover, Veer Singh Panwar
The matrix , has gained importance lately due to its role in powers preserving total nonnegativity. We give an ex…
Subdifferential set of the joint numerical radius of a tuple of matrices
Priyanka Grover, Sushil Singla
An expression for the subdifferential set of the joint numerical radius of a tuple of matrices is obtained. Its applications to the Birkhoff-James orthogonality in the space consis…
Best approximations, distance formulas and orthogonality in C*-algebras
Priyanka Grover, Sushil Singla
For a unital -algebra and a subspace of , a characterization for a best approximation to an element of in is ob…
Birkhoff-James orthogonality and applications : A survey
Priyanka Grover, Sushil Singla
In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficien…
Positivity properties of some special matrices
Priyanka Grover, Veer Singh Panwar, A Satyanarayana Reddy
It is shown that for positive real numbers , , where denotes the beta function, is infinitely divisi…
Orthogonality to matrix subspaces, and a distance formula
Priyanka Grover
We obtain a necessary and sufficient condition for a matrix to be Birkhoff-James orthogonal to any subspace of . Using this we obtain an ex…
Perturbation bounds for the Mostow and the bipolar decompositions
Priyanka Grover, Pradip Mishra
Perturbation bounds for Mostow's decomposition and the bipolar decomposition of matrices have been computed. To do so, expressions for the derivative of the geometric mean of two p…
Orthogonality of matrices in the Ky Fan -norms
Priyanka Grover
We obtain necessary and sufficient conditions for a matrix to be Birkhoff-James orthogonal to another matrix in the Ky Fan -norms. A characterization for to be Birkh…
Norm inequalities related to the matrix geometric mean
Rajendra Bhatia, Priyanka Grover
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
Derivatives of tensor powers and their norms
Rajendra Bhatia, Priyanka Grover, Tanvi Jain
The norm of the th derivative of the map that takes an operator to its th antisymmetric tensor power is evaluated. The case has been studied earlier by Bhatia and Fried…