[Solved] Given the following code, what will be the shape of the matrix U returned by svds? import numpy as np from scipy.... Given the following code, what will be the shape of the matrix U returned by svds? | SciPy

SciPy - Sparse Linear Algebra

Given the following code, what will be the shape of the matrix U returned by svds?

import numpy as np
from scipy.sparse.linalg import svds
from scipy.sparse import csr_matrix

A = csr_matrix(np.array([[1, 0, 0], [0, 2, 0], [0, 0, 3]]))
U, S, Vt = svds(A, k=2)

A(3, 3)

B(3, 2)

C(2, 3)

D(2, 2)

Step-by-Step Solution

Solution:

Step 1: Understand svds output shapes
For an input matrix of shape (m, n) and parameter k, svds returns U with shape (m, k), S with length k, and Vt with shape (k, n).
Step 2: Apply to given matrix
Matrix A is 3x3, k=2, so U shape is (3, 2).
Final Answer:
(3, 2) -> Option B
Quick Check:
U shape = (rows, k) = (3, 2) [OK]

Quick Trick: U shape is (rows, k) where k is number of singular values [OK]

Common Mistakes:

Confusing U shape with Vt shape
Assuming U is square matrix
Mixing up k with matrix dimensions

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Given the following code, what will be the shape of the matrix U returned by svds?

Step 1: Understand svds output shapes

Step 2: Apply to given matrix

Final Answer:

Quick Check:

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