Heatmap presenting the role random matrix played in matrix multiplication.

Zhang, Qi-Xin; Liu, Tianzi; Guo, Xinxin; Zhen, Jianxin; Yang, Meng-yuan; Khederzadeh, Saber; Zhou, Fang; Han, Xiaotong; Zheng, Qiwen; Jia, Peilin; Ding, Xiaohu; He, Mingguang; Zou, Xin; Liao, Jia-Kai; Zhang, Hongxin; He, Ji; Zhu, Xiaofeng; Lu, Daru; Chen, Hongyan; Zeng, Changqing; Liu, Fan; Zheng, Hou-Feng; Liu, Siyang; Xu, Hai-Ming; Chen, Guo-Bo

doi:10.1371/journal.pgen.1011037.s002

pgen.1011037.s002.pdf (545.03 kB)

Heatmap presenting the role random matrix played in matrix multiplication.

journal contribution

posted on 2024-01-11, 19:00 authored by Qi-Xin Zhang, Tianzi Liu, Xinxin Guo, Jianxin Zhen, Meng-yuan Yang, Saber Khederzadeh, Fang Zhou, Xiaotong Han, Qiwen Zheng, Peilin Jia, Xiaohu Ding, Mingguang He, Xin Zou, Jia-Kai Liao, Hongxin Zhang, Ji He, Xiaofeng Zhu, Daru Lu, Hongyan Chen, Changqing Zeng, Fan Liu, Hou-Feng Zheng, Siyang Liu, Hai-Ming Xu, Guo-Bo Chen

We generate a random matrix S_m×k sampling from N(0,1/k) and plot SS^T (B) against an identity matrix (A). We also generate two small populations containing 20 and 25 individuals, respectively. Their genotype matrices are noted as X₁ and X₂, and plot the matrix multiplication product before (C) and after encryption (D). The column number for the random matrix is k = 500 and the number of SNPs is m = 100.