Improving the Space-Time Efficiency of Matrix Multiplication Algorithms

Author(s):  
Yuan Tang
Author(s):  
Garima Srivastava ◽  
Rashmi Gupta ◽  
Raghvendra Kumar ◽  
Dac-Nhuong Le

There are several non-associative finite dimensional division algebras over different number fields. Their representations in the corresponding matrix algebras preserve additive structure. However, the embedding does not preserve multiplication as matrix multiplication is associative. As such, it gives a generalized matrix representation. Indeed, a non-associative structure provides different platforms for more effective and useful space-time coding satisfying rank criteria, and coding gain criteria for multiple antenna wireless communication. Associative division algebras have dimension restrictions, whereas non-associative division algebras over suitable fields exist in infinitely many dimensions. We illustrate the above program by using octonion algebras.


2013 ◽  
Vol 31 ◽  
pp. 112-130 ◽  
Author(s):  
Zhixiang Fang ◽  
Qiuping Li ◽  
Qingquan Li ◽  
Lee D. Han ◽  
Shih-Lung Shaw

2002 ◽  
Author(s):  
J. B. Kennedy
Keyword(s):  

Author(s):  
Roger Penrose ◽  
Wolfgang Rindler
Keyword(s):  

2018 ◽  
Vol 77 (4) ◽  
pp. 173-184
Author(s):  
Wenxing Yang ◽  
Ying Sun

Abstract. The causal role of a unidirectional orthography in shaping speakers’ mental representations of time seems to be well established by many psychological experiments. However, the question of whether bidirectional writing systems in some languages can also produce such an impact on temporal cognition remains unresolved. To address this issue, the present study focused on Japanese and Taiwanese, both of which have a similar mix of texts written horizontally from left to right (HLR) and vertically from top to bottom (VTB). Two experiments were performed which recruited Japanese and Taiwanese speakers as participants. Experiment 1 used an explicit temporal arrangement design, and Experiment 2 measured implicit space-time associations in participants along the horizontal (left/right) and the vertical (up/down) axis. Converging evidence gathered from the two experiments demonstrate that neither Japanese speakers nor Taiwanese speakers aligned their vertical representations of time with the VTB writing orientation. Along the horizontal axis, only Japanese speakers encoded elapsing time into a left-to-right linear layout, which was commensurate with the HLR writing direction. Therefore, two distinct writing orientations of a language could not bring about two coexisting mental time lines. Possible theoretical implications underlying the findings are discussed.


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