This paper gives three formulas for the pseudoinverse of a matrix product $A = CR$. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse $A^+_r$ may be very useful when $A$ is a very large matrix. 1. $A^+ = R^+C^+$ when $A = CR$ and $C$ has independent columns and $R$ has independent rows. 2. $A^+ = (C^+CR)^+(CRR^+)^+$ is always correct. 3. $A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+$ only when $\mathrm{rank}(P^TA) = \mathrm{rank}(AQ) = \mathrm{rank}(A)$ with $A = CR$.

翻译：本文给出了矩阵乘积$A=CR$的伪逆的三个公式。第一个公式有时正确，第二个公式始终正确，第三个公式几乎从不正确。但当$A$为超大规模矩阵时，第三种随机化伪逆$A^+_r$可能非常有用。1. 当$A=CR$且$C$列满秩、$R$行满秩时，有$A^+=R^+C^+$。2. $A^+ = (C^+CR)^+(CRR^+)^+$始终成立。3. 仅当$\mathrm{rank}(P^TA) = \mathrm{rank}(AQ) = \mathrm{rank}(A)$且$A=CR$时，$A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+$。