Linear Algebra quant interview questions

Linear algebra questions come up in quant research and quant developer interviews, especially for roles involving portfolio construction, statistical modelling and machine learning. Expect eigenvalues and eigenvectors, positive definiteness of covariance matrices, projections and least squares, matrix decompositions, rank and determinants, and quick reasoning about special matrices. Interviewers often ask for intuition, such as what an eigenvector of a covariance matrix represents or why a correlation matrix must be positive semi-definite. The problems here build from computational warm-ups to conceptual questions linked to finance and statistics. Free problems include hints and worked solutions showing each step. Practise them to strengthen the foundation behind regression, principal component analysis and risk models that appear throughout quant research interviews.