Topic
Transpose
About: Transpose is a research topic. Over the lifetime, 1572 publications have been published within this topic receiving 29313 citations. The topic is also known as: matrix transpose & transpose of a matrix.
Papers published on a yearly basis
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Papers
1 Jan 1985
TL;DR: This book presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
21,426 citations
Book•
1 Jan 1992TL;DR: The Radix-2 Frameworks, a collection of general and high performance FFTs designed to solve the multi-Dimensional FFT problem of Prime Factor and Convolution, are presented.
Abstract: 1. The Radix-2 Frameworks. Matrix Notation and Algorithms The FFT Idea The Cooley-Tukey Factorization Weight and Butterfly Computations Bit Reversal and Transposition The Cooley-Tukey Framework The Stockham Autosort Frameworks The Pease Framework Decimation in Frequency and Inverse FFTs 2. General Radix Frameworks. The General Radix Ideas Index Reversal and Transposition Mixed-Radix Factorizations Radix-4 and Radix-8 Frameworks The Split-Radix Frameworks 3. High Performance Frameworks. The Multiple DFT Problem Matrix Transposition The Large Single-Vector FFT Problem Multi-Dimensional FFT Problem Distributed Memory FFTs Shared Memory FFTs 4. Selected Topics. Prime Factor FFTs Convolution FFTs of Real Data Cosine and Sine Transforms Fast Poisson Solvers Bibliography Index.
1,468 citations
TL;DR: The biconjugate gradient method for solving general non-Hermitian linear systems and its transpose-free variant, the conjugate gradients squared algorithm (CGS), both typically exhib...
Abstract: The biconjugate gradient method (BCG) for solving general non-Hermitian linear systems $Ax = b$ and its transpose-free variant, the conjugate gradients squared algorithm (CGS), both typically exhib...
699 citations
TL;DR: It is shown that, for systems composed of a single oscillator for Alice and an arbitrary number for Bob, positivity of the partial transpose implies separability, but this implication fails with two oscillators on each side, as it is shown by constructing a five parameter family of bound entangled Gaussian states.
Abstract: We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. For the separability, and the positivity of the partial transpose, we establish explicit necessary and sufficient criteria in terms of the covariance matrix of the state. It is shown that, for systems composed of a single oscillator for Alice and an arbitrary number for Bob, positivity of the partial transpose implies separability. However, this implication fails with two oscillators on each side, as we show by constructing a five parameter family of bound entangled Gaussian states.
535 citations
11 Aug 2009
TL;DR: In this article, a storage format for sparse matrices, called compressed sparse blocks (CSB), is introduced, which allows both Ax and A,x to be computed efficiently in parallel, where A is an n×n sparse matrix with nnzen nonzeros and x is a dense n-vector.
Abstract: This paper introduces a storage format for sparse matrices, called compressed sparse blocks (CSB), which allows both Ax and A,x to be computed efficiently in parallel, where A is an n×n sparse matrix with nnzen nonzeros and x is a dense n-vector. Our algorithms use Θ(nnz) work (serial running time) and Θ(√nlgn) span (critical-path length), yielding a parallelism of Θ(nnz/√nlgn), which is amply high for virtually any large matrix. The storage requirement for CSB is the same as that for the more-standard compressed-sparse-rows (CSR) format, for which computing Ax in parallel is easy but A,x is difficult. Benchmark results indicate that on one processor, the CSB algorithms for Ax and A,x run just as fast as the CSR algorithm for Ax, but the CSB algorithms also scale up linearly with processors until limited by off-chip memory bandwidth.
458 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 18 |
| 2024 | 41 |
| 2023 | 92 |
| 2022 | 169 |
| 2021 | 63 |
| 2020 | 80 |