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
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
+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.
+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?
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Elegant, clear, brimming with insight, a real gift of a lecture.
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
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
Just one word for this lecture. Beautiful
Thank you!
Great. Extremely nice explanation. Thanks
Really good explanation, thank you :)
+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.
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.
Hi, my English isn't well, could professor write down the explanation of eigen value of the Q?
+thentust Your English is great, but I'm not quite sure what your question is.
+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?
How can we be sure other professors even understand linear algebra?
Matrix be like : I am a matrix, I'm burdened with glorious purposes