Recent content by hellomrrobot

What does it mean when it says to classify the second-order partial differential? (See attached) How would I get started?

Homework Statement There is a typo in the problem, ”R > Σ n i=1 σi − n max 1≤i≤n σi” which should be R > n max (1≤i≤n) σi − (Σ n i=1 σi ) Homework EquationsThe Attempt at a Solution Not sure where to go with part B or where to start...

anti-symmetric?

I am having trouble showing that ##(A_{ik}B_{kj})_{mm} = (A_{ki}B_{jk})_{mm}## Wouldn't the right side end up having a different outcome? Or can we assume its symmetric?

Yes, but what does that look like? It has been a while since I have even used the word eigenvalue/vector...

What does it mean when it says eigenvalues of Matrix (3x3) A are the square roots of the eigenvalues of Matrix (3x3) B and the eigenvectors are the same for A and B?

I am confused at why ##V_{i,j}V_{j,k}A_{km,i}## the result will end up being a vector (V is a vector and A is a tensor) What are some general rules when you are multiplying a scalar, vector and tensor?

Okay so after I do the summation, I would get ##(dp/dx_{1})A\delta_{i1} + (dp/dx_{2})A\delta_{i2} + (dp/dx_{3})A\delta_{i3}## Then if I set i=1, I would get just ##dp/dx_{1}## ?

How would the partial derivative look like? This is what I got ##(dp/dx_{j}) \delta_{ij} + p (d \delta_{ij}/dx_{j})##

Can anyone explain how to take the derivative of (Aδij),j? I know that since there is a repeating subscript I have to do the summation then take the derivative, but I am not sure how to go about that process because there are two subscripts (i and j) and that it is the Kronecker's Delta (not...