/sci/ - Science & Math

>>11701567
>>11701891
Never mind, the trick is completely different.
So, we'll use [math]||x-y||^2 = ||x||^2 + ||y||^2 - 2 \langle x, y \rangle [/math].
The matrix [math]A[/math] has collumns [math]A_i[/math] and entries [math]A_{i, j}[/math].
[math]||A_i - A_j||^2 = ||A_i||^2 + ||A_j||^2 - 2 \langle A_i, A_j \rangle [/math].
For the last term, we notice that [math][A^T A]_{i, j} = \langle A_i, A_j \rangle [/math].
Then, we add in [math]diag (A^T A)1_n^T[/math], which is the matrix whose i-th rows is constantly [math]||A_i||^2[/math], and [math]1_n diag(A^TA)^T[/math], the matrix whose i-th collumn is constantly [math]||A_i||^2[/math].
So [math]D(X)= - 2 A^T A + diag (A^T A)1_n^T + 1_n diag(A^TA)^T[/math]
That should be it, I think.

>>11626247
And the noncompact ones are Stein spaces.

>>11588378
Ehhh, there was some hidden here and there.
BTW, this dude asked for a summary of inverse problems for PDEs and I gave him a shitty reply about it.
Anyone wanna hold his hand through it?