6. Linear Algebra: Vector Spaces and Operators (continued)

MIT 8.05 Quantum Physics II, Fall 2013
Instructor: Barton Zwiebach

In this lecture, the professor talked about linear operators and matrices, etc.

License: Creative Commons BY-NC-SA

[matthewsarsam]

At 39:31 this is range null space decomposition. You only get a full decomposition of the input space as a direct sum of the nullspace and range when the nullspace of T^2 is the same as T. If the nullspace grows, you have a non zero intersection

[a.c.e]

Difference between Professor Zwiebach and this mate

Professor Zwiebach showing a property which is a bit unclear :"Now I will show the rigorous mathematical proof and answer any questions you have and also do additional proofs and show the correspondence between all I taught this session so it's all clear and everyone is happy."

This mate :"So the proof of this is non-trivial, and I'm not gonna show how to do it or derive it."

Professor actually allows you to understand deeply how the equations are formed, I LOVE how he assumes that nothing is completely clear and explains every little thing. I would say god bless him, I love his lectures and he is by far THE best lecturer I have seen in Quantum Mathematics. Thank you so much Professor, you have made my sleepless nights a delight from a waking nightmare of worry and sickness. Thank you so much, I really don't know what to say. Thank you

[Zealot]

About right shift, I checked, if I put x1 to the left, it is still a linear operator. And even more, I can put result of linear operator T(x1, x2, ...) to the left, it is still linear

[kilianklaiber]

I think this was a great lecture. I could follow everything but I studied linear algebra many years ago. He covered so much material I wonder how the students were capable of following him, if this was new to them.

[ROOPESHWARMEGADULA]

It was a mistake expanding TVj at 57:06 in terms of the same eigenbasis as before transformation, as it should be developed in terms of the eigenbasis of the transformed vector space.

[manaoharsam]

It is a nice lecture. But my knowledge is needs refinement. This means

1 review video again and think about it

2 if there are any subtle features look at other books.

Being an Engineer I am familiar with vectors and matrix algebra, but I think I need investigate further.


But in general this has been a fantastic course so far. Everyone did a grand job.

[yyc]

Is the relation at 57:48 (Tvj)=ΣT_ji·v_j) only valid for the orthogonal bases?

[qwertycorno]

Eigenvalues and Eigenvectors are named after Dr. Heinrich Eigen, a German mathematician.

[zarchy]

I'm having trouble convincing myself that the left-shift operator is a linear operator. If I have two series, A and B, and I apply the operator to each series individually, and then sum the results, I will lose the first term from each sequence. If I sum the two series first and then apply the operator, I will lose only one term. What am I missing?

[awhenpeter]

sorry sir almost all of you in MIT has terrible writing