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@darrenpeck156
2 жыл бұрын
Elegant, clear, brimming with insight, a real gift of a lecture.
@aleksandarlukac8868
6 жыл бұрын
Mr Pavel Grinfeld, thank you so much for your passionate and breathtaking explanations that make me speechless. I am thankful for modern internet age that i can follow such interesting subject. So far i just learned definition of orthogonal matrices and i knew what they are, but i did not know motivation and how somebody came up with such concept. with this video i will whole my life forever know what orthogonal matrices are and what are used for. i will watch all your brilliant videos, and i am very thankful on them
@MathTheBeautiful
6 жыл бұрын
Hi Aleksandar, Thank you for your comment. I'm glad you find my videos helpful. I have students just like you in mind who are trying to understand the underlying principles. Pavel
@Sachdev23
7 күн бұрын
Just one word for this lecture. Beautiful
@MathTheBeautiful
7 күн бұрын
Thank you!
@AmarSingh-ln6ie
3 жыл бұрын
Great. Extremely nice explanation. Thanks
@siminho6929
3 жыл бұрын
Really good explanation, thank you :)
@vinylflouring
11 ай бұрын
How can we be sure other professors even understand linear algebra?
@tangolasher
7 жыл бұрын
+MathTheBeautiful The algebraic way you arrive at QTQ = I couldve been applied to any matrix transformation, am I right? Because it's just based on the fact that Transpose of a product of two matrices = the product of their transposes in reverse order, which holds for *any* matrix. However, QtQ = I *clearly* does not hold for just *any old matrix.* So the way you make this jump seems invalid. Could you please explain why this works? Thanks.
@agilanamirthalingam8418
4 жыл бұрын
this is late but anyway... The property used here is any square matrix commutes with its inverse. Here the inverse happens to be the transpose.
@thentust
8 жыл бұрын
Hi, my English isn't well, could professor write down the explanation of eigen value of the Q?
@MathTheBeautiful
8 жыл бұрын
+thentust Your English is great, but I'm not quite sure what your question is.
@thentust
8 жыл бұрын
+MathTheBeautiful My question is figured out. and I have another question: You said: "eigen values of the Q are really the same as the eigen values of the linear transformation Q ." ?? I thought Q is already a linear transformation matrix,what is linear transformation Q? Q*Q?
@ektabansal7109
Жыл бұрын
Matrix be like : I am a matrix, I'm burdened with glorious purposes
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