eigenvalue

Vocabulary Word

Definition

'Eigenvalue' is a mathematical concept from linear algebra. It's a special number, when multiplied to a vector, changes its magnitude (length) but not direction. Think of stretching or shrinking a photo but keeping it upright.

Examples in Different Contexts

In financial modeling, 'eigenvalue' analysis can be used for risk assessment and portfolio optimization. A financial analyst might state, 'By studying eigenvalues, we can discern the volatility levels inherent in our investment portfolio’s asset mix.'

Practice Scenarios

Tech

Scenario:

We need to manage the dimensions of this machine learning model and reduce computational complexity.

Response:

We can find the eigenvalues to decompose the higher-dimensional data and apply Principal Component Analysis.

Business

Scenario:

Building a diversified portfolio requires getting a hold on risk and also maximizing returns.

Response:

Calculating the eigenvalues of the covariance matrix would aid us in mitigating portfolio risk while optimizing returns.