# linear algebra – why does this equivalence hold \$X-Ysucccurlyeq 0 iff begin{pmatrix}X & 1\1 & Y^{-1} end{pmatrix}succcurlyeq 0\$

I’m struggeling to see that for two symmetric matrices $$X,Y$$ the following two conditions should be equivalent:

$$X-Ysucccurlyeq 0 iff begin{pmatrix}X & 1\1 & Y^{-1} end{pmatrix}succcurlyeq 0$$

where $$Xsucccurlyeq 0$$ reads as $$X$$ being positive semi definite