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Review 1
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Average rating 5.0
It was a high-quality class that was on a different level from undergraduate classes. In particular, you may feel resistance at the beginning because of the unfamiliar English words, but if you listen to the lectures and review consistently, you will gradually understand the concepts, and there will be a point where the formulas and theorems will be clearly understood. In particular, the concepts gradually expand with each unit, and I was really impressed by the fact that all of this was a build-up for SVD. I am envious of how great it would have been if I had a class like this when I was an undergraduate. Starting from the first unit, you solve the augmented matrix as a general solution by row reduction, or the rank, dimension, determinant, eigenvalue, eigenvector, orthogonality, Gram-Schmidt, diagonalization and spectral decomposition, symmetric matrix, quadratic form of the matrix. The knowledge learned in all units is organically connected and used in amazing organization and proof. Personally, I really liked the part where they compared the numerical efficiency, memory efficiency, and time complexity of various decomposition algorithms (LU, PA=LU, QR). I thought linear algebra was simply a discipline that expressed linear equations as matrix equations and found solutions, but I think it was really helpful to see how it looks geometrically and how it is applied in engineering practice, such as various algorithms to more efficiently find matrix solutions, how to fit data linearly by minimizing error values through least-squares, how to find the maximum value of a matrix by applying constraints in quadratic form, and how to compress data more efficiently through SVD. I'm really looking forward to the probability and statistics and vector calculus classes in the future. I'm also looking forward to the numerical analysis lecture! Thank you so much for providing such a great lecture.