Something you take as intuitivly obvious really isn't that obvious at all...
A friend of mine and I were talking about solving for mesh currents (in a completely resistive circuit) VIA using a matrix. Now its routinely taken for granted that this matrix is invertable (IE non-singular). However, this is not intuitivly obvious. I was wondering if someone could show for the NxN case that the matrix MUST be non-singular, also would it then be positive definite? I believe that it is not only non-singular but it must also be positive definite...
I've shown for the 2x2 case that it MUST be non-singular, however I haven't found a way to show it generally. I'm still thinking about it though... :?
A friend of mine and I were talking about solving for mesh currents (in a completely resistive circuit) VIA using a matrix. Now its routinely taken for granted that this matrix is invertable (IE non-singular). However, this is not intuitivly obvious. I was wondering if someone could show for the NxN case that the matrix MUST be non-singular, also would it then be positive definite? I believe that it is not only non-singular but it must also be positive definite...
I've shown for the 2x2 case that it MUST be non-singular, however I haven't found a way to show it generally. I'm still thinking about it though... :?