FoundationNumeric answer
A covariance matrix has eigenvalues , , and . What percentage of total variance does the first principal component explain?
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
The worked solution is in Premium
The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.
Learn the method
PCA, covariance matrices and what an eigenvalue is telling you
More linear algebra questions
- Keeping the big singular values, part 1 of 3Foundation
- You run PCA on yield-curve changes across maturities. What is the first component?Applied
- A matrix has largest singular value 100 and smallest 0.5. What is its condition number?Applied
- Keeping the big singular values, part 2 of 3Applied
- You estimate a 500 × 500 sample covariance matrix from 250 days of demeaned returns.Advanced
- You run PCA on raw features measured in wildly different units, and one feature…Advanced