Mastery Challenge

Advanced Concepts

Dive deeper into eigenvectors, matrix decompositions, spectral theorems, and advanced linear algebra properties essential for ML.

1

Eigenvalues

For a diagonal matrix D = [[3, 0], [0, 5]], what are the eigenvalues?

2

Orthogonal Matrices

If matrix Q is orthogonal (Q^T = Q^-1), what is the value of the determinant of Q?

3

Singular Value Decomposition

In the SVD of A = UΣV^T, the columns of matrix U are called the:

4

Positive Definite Matrices

A symmetric matrix A is positive definite if and only if all of its eigenvalues are: