Find the singular value decomposition of A = [ (3 2 2), (2 3 2)
] and determine the angle of rotation induced by U and V . Also,
write the rank 1 decomposition of A in terms of the columns of U
and rows of V . Can we do dimensionality reduction in this
case?
Obtain a spectral decomposition for the symmetric matrix A = [0
2 2, 2 0 2, 2 2 0] (that means the first row is 022, then below
that 202, etc.) , whose characteristic polynomial is −(λ + 2)^2 (λ
− 4)
If you could provide a step-by-step way to solve this I'd
greatly appreciate it.
Question. Programming question: Dimension Reduction
In this question, you are asked to run Singular Value Decomposition
(SVD) on Fashion-MNIST data set, interpret the output and train
generative classifiers for multi- nomial classification of 10
classes. For the Fashion-MNIST data set, you can find more details
in the original GitHub website or Kaggle website. In this
assignment, you are allowed to use a library implementation of SVD.
For python users, we recommend scikit-learn’s implementation
TruncatedSVD.
Tasks:
?Load the training and test...
Question. Programming question: Dimension Reduction
In this question, you are asked to run Singular Value Decomposition
(SVD) on Fashion-MNIST data set, interpret the output and train
generative classifiers for multi-nomial classification of 10
classes. For the Fashion-MNIST data set, you can find more details
in the original GitHub website or Kaggle website.
Kaggle: https://www.kaggle.com/zalando-research/fashionmnist
GetHub: https://github.com/zalandoresearch/fashion-mnist
Tasks:
?Load the training and test data sets from fashion-mnist
train.csv and fashion- mnist test.csv. Each row uses a vector of
dimension 784 with...
(a) Show that x= 0 is a regular singular point.
(b) Find the indicial equation and the indicial roots of it.
(c) Use the Frobenius method to and two series solutions of each
equation
x^2y''+xy'+(x^2-(4/9))y=0
LU Decomposition
(i). Prove that for n equal to 2 or 3 there is a non-singular
square (n by n) matrix which has no LU decomposition with L unit
lower triangular and U upper triangular. (In fact, this is true for
any integer ≥ 2.)
(ii). We will see that all non-singular square matrices do have
an LUP decomposition (some time soon in class). Here P is a
permutation matrix, also defined in Appendix D and used in Chapter
28....