On the Trace of Matrix Products

1959 ◽  
Vol 20 (3-6) ◽  
pp. 171-174 ◽  
Author(s):  
Leon Mirsky
Keyword(s):  
Matrix Products ◽  
Trace Of Matrix

An inequality for the trace of matrix products

1974 ◽  
Vol 6 (2) ◽  
pp. 225-235 ◽  
Author(s):  
H.W Capel ◽  
P.A.J Tindemans
Keyword(s):  
Matrix Products ◽  
Trace Of Matrix

scholarly journals A low-area high-efficiency video coding inverse transform core using resource and time sharing architecture

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuan-Ho Chen ◽  
Chieh-Yang Liu
Keyword(s):  
Video Coding ◽  
Large Scale ◽  
High Efficiency ◽  
Vlsi Design ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Time Sharing ◽  
High Efficiency Video Coding ◽  
Low Area ◽  
Matrix Products

AbstractIn this paper, a very-large-scale integration (VLSI) design that can support high-efficiency video coding inverse discrete cosine transform (IDCT) for multiple transform sizes is proposed. The proposed two-dimensional (2-D) IDCT is implemented at a low area by using a single one-dimensional (1-D) IDCT core with a transpose memory. The proposed 1-D IDCT core decomposes a 32-point transform into 16-, 8-, and 4-point matrix products according to the symmetric property of the transform coefficient. Moreover, we use the shift-and-add unit to share hardware resources between multiple transform dimension matrix products. The 1-D IDCT core can simultaneously calculate the first- and second-dimensional data. The results indicate that the proposed 2-D IDCT core has a throughput rate of 250 MP/s, with only 110 K gate counts when implemented into the Taiwan semiconductor manufacturing (TSMC) 90-nm complementary metal-oxide-semiconductor (CMOS) technology. The results show the proposed circuit has the smallest area supporting the multiple transform sizes.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

scholarly journals Factorizations for q-Pascal matrices of two variables

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Thomas Ernst
Keyword(s):  
Matrix Products ◽  
Natural Way

AbstractIn this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as followsWe also find two different matrix products for

Trace Forms on Lie Algebras

1962 ◽  
Vol 14 ◽  
pp. 553-564 ◽  
Author(s):  
Richard Block
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Bilinear Form ◽  
Symmetric Bilinear Form ◽  
Trace Form ◽  
Finite Degree ◽  
Trace Forms ◽  
Matrix Products ◽  
The Matrix ◽  
Image Position

If L is a Lie algebra with a representation Δ a→aΔ (a in L) (of finite degree), then by the trace form f = fΔ of Δ is meant the symmetric bilinear form on L obtained by taking the trace of the matrix products:Then f is invariant, that is, f is symmetric and f(ab, c) — f(a, bc) for all a, b, c in L. By the Δ-radical L⊥ = L⊥ of L is meant the set of a in L such that f(a, b) = 0 for all b in L. Then L⊥ is an ideal and f induces a bilinear form , called a quotient trace form, on L/L⊥. Thus an algebra has a quotient trace form if and only if there exists a Lie algebra L with a representation Δ such that

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