Linear Algebra 20c: Length Expressed in a non-Cartesian Basis

[anantgairola]

Omg! It's the metric tensor! Isn't it? That matrix in the middle! It has to be a 2x2 matrix to make the product consistent. It's pre-multiplied with alpha (multiplied from the left) so by using the row perspective for matrix multiplication we can figure out that it's the pair-wise dot product of the basis elements. I know technically we haven't defined dot product in this course yet but in tensors that's how the metric tensor Zij was introduced. I knew this course and the one on tensors will come together in my mind at some point! It's happening wish I went to Drexel! :)

[karl-heinzk]

Hi,  
I have a hard time to understand why around 4:00 min the component alpha1 is entered as 3 times alpha1 into the equation. To my understanding the length is alpha1 times beta1 in the non-cartesian basis. In this special case alpha1 is around 1 unit length (with beta being 3 units long) which is 1/3 relative to  beta1. Why do you not enter this length (1/3 alpha1 relative to beta1) into the equation of Pythagoras? I do not see where from the scaler 3 is coming (instead of 1/3). Could you please explain this with a few more words?
Thanks a lot for all the efforts with this video lectures!!!
Karl-Heinz 

[sharmaabhi]

Hi Prof Grinfeld..once again deep compliments for excellent set of lectures. Truly awesome!! But one q I have: in one of previous videos it was mentioned we would take up the block matrices. But can't see coming in any of the further lectures. Request address.

[tangolasher]

+MathTheBeautiful
Will you answer the question you posed at the end of this video eventually? If not, could you please post the answer, because I'm terrified of not knowing the answer to that question and I have no idea how to find it. Thanks.