Topics in Matrix Analysis

By Roger A. Horn, Charles R. Johnson. 1991

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, methodology): “We also use the Hadamard product identity diag Horn and Johnson [1991].”
On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, neutral): “More generally, any mixture of ˜ D ( λ ) over λ ≥ 0 is a squared Euclidean distance, yielding the following deﬁnition and theorem: where g ( λ ) dλ is a non-negative measure on [0 , ∞ ) such that λ dλ ∞ .”
Communication-efficient algorithms for decentralized and stochastic optimization (2017, neutral): “12 in [24], L is symmetric positive semidefinite and its null space coincides with the “agreement” subspace, i.”
User-Friendly Tail Bounds for Sums of Random Matrices (2010, background): “The works of Horn and Johnson [22, 23] also serve as good general references.”
Gradient Descent with Identity Initialization Efficiently Learns Positive-Definite Linear Transformations by Deep Residual Networks (2018, neutral): “com June 19, 2018 Abstract We analyze algorithms for approximating a function f(x) = Φxmapping R to R using deep linear neural networks, i.e. that learn a function h parameterized by matrices Θ1, ...,ΘL and defined by h(x) = ΘLΘL−1...Θ1x. We focus on algorithms that learn through gradient descent on”
Shampoo: Preconditioned Stochastic Tensor Optimization (2018, background): “For proofs and further details, we refer to [12].”
The graphs for which the maximum multiplicity of an eigenvalue is two (2007, background): “Now, identify the three neighbors of ualong the path P1, P2, and P3 together with uand vto give the set Scontained among the vertices of G. Let A∈ S(G) be chosen as follows: A[Sc] is an M-matrix (see [7], Ch. 2), the three edges from uto its neighbors in Sare free, the diagonal entries corresponding”
Analysis and Numerical Solution of Generalized Lyapunov Equations (2002, background): “is the matrix representation of the discrete-time Lyapunov operator Ld, see [78].”
A new primal-dual path-following interior-point algorithm for semidefinite optimization (2009, background): “For the details we refer to the book [9].”
Synchronization in networks of identical linear systems (2008, background): “[16]) and the passivity relation (18) we obtain”
A Convergence Analysis of Log-Linear Training (2011, unknown): “[8]): HF (Λ0) = S⊗X .”