Yes indeed. One definition of a PSD matrix is some matrix M such that, for any vector X, XTMX≥0 (so, it defines some kind of scalar product).
If Mi,i=y, then you can always divide the whole row/column by √y, which is equivalent to applying some scaling, this won’t change the fact that M is PSD or not.
If Mi,i=−1, then if you try the vector X:∀j≠i,Xj=0;Xi=1, you can check that XTMX=−1, thus the matrix isn’t PSD.
Yes indeed. One definition of a PSD matrix is some matrix M such that, for any vector X, XTMX≥0 (so, it defines some kind of scalar product).
If Mi,i=y, then you can always divide the whole row/column by √y, which is equivalent to applying some scaling, this won’t change the fact that M is PSD or not.
If Mi,i=−1, then if you try the vector X:∀j≠i,Xj=0;Xi=1, you can check that XTMX=−1, thus the matrix isn’t PSD.