Recent content by Lonely Lemon

It's the identity matrix, but \delta_{rn} could be either 0 or 1 depending on if r=n or r=/=n... EDIT r=/=n

There's nothing special about C, the exercise is to just get us used to index notation and what it means I think but I'm struggling a bit. The next question is: A_{ij}B_{nk}C_{rs}\delta_{jr}\delta_{sn}\delta_{ik} but I can't do that until I figure out how to work with delta above...

Homework Statement Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices. C_{ns}\delta_{rn} Homework Equations The Attempt at a Solution I know Kronecker delta is symmetric but that doesn't seem to help. Is...

I assume so, that's the problem posed word for word. T: R3-->R3 is the linear transformation determined by a 3x3 matrix A, and S is the a parallelepiped in R3, so the vectors define both?

Homework Statement If S is a parallelepiped determined by v1=(1, 1, 0) and v2= (3, 2, 1) and v3=(6, 1, 2) and T: R3--> R3 by T(x)=Ax, find the volume of T(S) Homework Equations {volume of T(S)}=|det A|.{volume of S} The Attempt at a Solution A is [v1 v2 v3] and the |A| = 9 by my...

Ah, you're right! My textual representation did read [0 -2 -4] as a column, but if I do transpose the matrix I end up with the correct linear transformation. I can see how the answer comes about now, but I still don't see why I need to transpose my transformation matrix? Can you explain?

That's still not giving me the correct result... If I go [0 -2 -4; -2 0 2; 0 0 1][0 0 1] for example [0 0 1] just shoots back out again, which can't be right when there is a translation involved

I did that, my homogeneous vector matrix for the triangle is, call it P: P = [0 0 1; 1 2 1; 2 3 1] But if I multiply the ABC matrix by P such that I get [0 -2 -4; 2 0 2; 0 0 1][0 0 1; 1 2 1; 2 3 1] I end up with [0 0 1; -4 -2 1; -6 -4 -1] which is patently wrong...

Homework Statement Write down 3x3 matrices A, B, C such that when the vectors in R2 are expressed in homogeneous coordinates, the product ABC first translates vectors by (-1, 2), then reflects them about the line y=-x and finally scales them by 2. using your matrix ABC, determine the image...

Oh, then we have (x^T)(y)=x.y I didn't realize you could break up the dot product components and just multiply them together

Okay, I get this far: (Ux).(Uy)=(x^T)(U^T).(y^T)(U^T) It's like drawing blood from a stone - I get stuck at every step...

I know that if U is orthogonal then (U^T)(U)=I, and by the Invertible Matrix Theorgem U inverse = U transpose?

Homework Statement Let U be an mxn matrix with orthonormal columns, and let x and y be in R^n. Prove (Ux).(Uy)=x.y Homework Equations I know ||Ux||^2=(Ux)^T(Ux) The Attempt at a Solution I just have no idea...

Never mind! Click! Just figured out I should have been going (I-A)(I-A)=... Thanks for the help

If I do that, I get to option C That is (I-A)(I-A)^-1=(I-A)/(I-A)=I which seems correct, but the answer is apparently E. I+A+A^2 *EDIT: Meant I+A+A^2