Motivated by the general matrix deviation inequality for i.i.d. ensemble Gaussian matrix [R. Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2018), doi:10.1017/9781108231596 of Theorem 11.1.5], we show that this property holds for the ${\ell }_p$-norm with $1\le p<\infty$ and i.i.d. ensemble sub-Gaussian matrices, i.e. random matrices with i.i.d. mean-zero, unit variance, sub-Gaussian entries. As a consequence of our result, we establish the Johnson–Lindenstrauss lemma from ${\ell }_2^n$-space to ${\ell }_p^m$-space for all i.i.d. ensemble sub-Gaussian matrices.

受 iid 系综高斯矩阵的一般矩阵偏差不等式的启发 [R。Vershynin，高维概率：数据科学应用简介，剑桥统计和概率数学丛书（剑桥大学出版社，2018 年），doi:10.1017/9781108231596 of Theorem 11.1.5]，我们表明此属性适用于${\ell }_p$-规范$\mathrm{1个}\le p<\infty$iid 集合亚高斯矩阵，即具有 iid 均值为零、单位方差、亚高斯条目的随机矩阵。作为我们结果的结果，我们建立了 Johnson-Lindenstrauss 引理${\ell }_{\mathrm{2个}}^n$-空间到${\ell }_p^{米}$-所有 iid 合奏子高斯矩阵的空间。