Reduction of a General Matrix to Tridiagonal Form

1991 ◽  
Vol 12 (2) ◽  
pp. 362-373 ◽  
Author(s):  
George A. Geist
Keyword(s):  
General Matrix ◽  
Tridiagonal Form

The canonical form of invariant matrices

1970 ◽  
Vol 68 (1) ◽  
pp. 21-25 ◽  
Author(s):  
D. B. Hunter
Keyword(s):  
Canonical Form ◽  
General Matrix ◽  
Invariant Matrices

1. Introduction. Let A[λ] be the irreducible invariant matrix of a general matrix of order n × n, corresponding to a partition (λ) = (λ1, λ2, …, λr) of some integer m. The problem to be discussed here is that of determining the canonical form of A[λ] when that of A is known.

scholarly journals Register-based implementation of the sparse general matrix-matrix multiplication on GPUs

2018 ◽  
Vol 53 (1) ◽  
pp. 407-408
Author(s):  
Junhong Liu ◽  
Xin He ◽  
Weifeng Liu ◽  
Guangming Tan
Keyword(s):  
Matrix Multiplication ◽  
General Matrix

scholarly journals Centrality-friendship paradoxes: when our friends are more important than us

2018 ◽  
Vol 7 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Desmond J Higham
Keyword(s):  
Network Science ◽  
Sufficient Conditions ◽  
Sampling Bias ◽  
Average Degree ◽  
Science Literature ◽  
Eigenvector Centrality ◽  
General Matrix ◽  
Theoretical Support ◽  
The Social ◽  
Katz Centrality

Abstract The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic example of sampling bias, has attracted much attention in the social science and network science literature, with variations and extensions of the paradox being defined, tested and interpreted. Here, we show that a version of the paradox holds rigorously for eigenvector centrality: on average, our friends are more important than us. We then consider general matrix-function centrality, including Katz centrality, and give sufficient conditions for the paradox to hold. We also discuss which results can be generalized to the cases of directed and weighted edges. In this way, we add theoretical support for a field that has largely been evolving through empirical testing.

A QR-type reduction for computing the SVD of a general matrix product/quotient

2003 ◽  
Vol 95 (1) ◽  
pp. 101-121 ◽  
Author(s):  
Delin Chu ◽  
Lieven De Lathauwer ◽  
Bart De Moor
Keyword(s):  
Matrix Product ◽  
General Matrix ◽  
Type Reduction

General matrix representations for B-splines

2000 ◽  
Vol 16 (3-4) ◽  
pp. 177-186 ◽  
Author(s):  
Kaihuai Qin
Keyword(s):  
Matrix Representations ◽  
General Matrix ◽  
B Splines
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