Hey random strangers in the u.s., i am a chinese who suffered depression. I am also passionate about math, music, coding and art! What I want to say is that take care of yourself. Every one's life is tough all over the world nowadays, it's not our problem. To motivate you with some math joy and provide you with some youtube video content, I here challenge you with a linear algebra problem that you may solve and post a youtube video on it. The problem reads: try to prove that for any real-valued symmetric matrix A, if A satisfied the condition that for all i,j, A_{ij} < max(A_{ii}, A_{jj}), then no matter if A is positive definite, there must be a real-valued symmetric positive definite matrix B that is so similar to A in the sense that for all i,j,m,n, if A_{ij}
My apologies, I made a mistake with the sign in the second step. It should be -2.
Hey random strangers in the u.s., i am a chinese who suffered depression. I am also passionate about math, music, coding and art! What I want to say is that take care of yourself. Every one's life is tough all over the world nowadays, it's not our problem. To motivate you with some math joy and provide you with some youtube video content, I here challenge you with a linear algebra problem that you may solve and post a youtube video on it. The problem reads: try to prove that for any real-valued symmetric matrix A, if A satisfied the condition that for all i,j, A_{ij} < max(A_{ii}, A_{jj}), then no matter if A is positive definite, there must be a real-valued symmetric positive definite matrix B that is so similar to A in the sense that for all i,j,m,n, if A_{ij}
no matter if A is positive definite or not