Linear Algebra Interview Questions
Linear algebra underpins modern quant modelling. These questions cover matrices, eigenvalues, and projections that appear in research and quant-developer interviews.
This area covers matrices and their operations, eigenvalues and eigenvectors, rank and null space, projections and least squares, and positive-(semi)definite matrices - concepts that recur in research and quant-developer interviews.
Questions reward geometric intuition: understanding what a matrix does to space, why eigenvectors matter, and how projections and least squares connect.
50 linear algebra questions · 28 free to practise now.
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- Angle under an orthogonal mapEasyLinear AlgebraView →
- Determinant after antisymmetrizingEasyProbabilityLinear AlgebraView →
- Determinant from trace and one eigenvalueEasyLinear AlgebraView →
- Determinant of a scaled productEasyLinear AlgebraView →
- Diagonal parameter from a triangular determinantEasyLinear AlgebraView →
- Eigenvalues of a 2×2 matrixEasyLinear AlgebraView →
- Largest eigenvalue after squaringEasyLinear AlgebraView →
- Length of a vector differenceEasyLinear AlgebraView →
- Norm after imposing orthogonalityEasyLinear AlgebraView →
- Parameter values for a singular matrixEasyLinear AlgebraView →
- Rank of a matrix productEasyLinear AlgebraView →
- Sum of cubed eigenvaluesEasyLinear AlgebraView →
- A Cholesky diagonal entryMediumLinear AlgebraView →
- A Gram–Schmidt R entryMediumLinear AlgebraView →
- A tenth power of a matrixMediumLinear AlgebraView →
- Eigenvalues of a projectionMediumLinear AlgebraView →
- Eigenvalues of a rotationMediumLinear AlgebraView →
- Growth rate of a rank-one eigenvalueMediumLinear AlgebraView →
- How large can the off-diagonal be?MediumLinear AlgebraView →
- Largest eigenvalue of a rank-one updateMediumLinear AlgebraView →
- Length of a projectionMediumLinear AlgebraView →
- Long-run share of a two-state chainMediumLinear AlgebraView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- Rank and nullity of a rotationMediumLinear AlgebraView →
- Smallest value of a quadratic formMediumLinear AlgebraView →
- Spectrum of a constant-diagonal matrixMediumLinear AlgebraView →
- Spectrum of a symmetric matrixMediumStatisticsLinear AlgebraView →
- Trace of a productMediumLinear AlgebraView →
- Area of a parallelogramMediumLinear Algebra Premium
- Cheapest way to chain three productsMediumLinear Algebra Premium
- Condition numberMediumLinear Algebra Premium
- Determinant of a 3×3MediumLinear Algebra Premium
- Determinant of a compound expressionMediumLinear Algebra Premium
- Determinant of an orthogonal matrixMediumLinear Algebra Premium
- Larger eigenvalue of a 2×2MediumLinear Algebra Premium
- Maximize x + y on the unit circleMediumLinear AlgebraCalculus Premium
- Maximum rate of increaseMediumLinear AlgebraCalculus Premium
- Nullity of a concrete matrixMediumLinear Algebra Premium
- Positive semidefinitenessMediumStatisticsLinear Algebra Premium
- Power iterationMediumLinear AlgebraProgramming & DSA Premium
- Projecting onto a lineMediumLinear Algebra Premium
- Rank–nullity dimension countMediumLinear Algebra Premium
- Recovering an eigenvector from its eigenvalueMediumLinear Algebra Premium
- Reducing a matrix power with Cayley–HamiltonMediumLinear Algebra Premium
- Singular values via AᵀAMediumLinear Algebra Premium
- Trace of A-transpose-AMediumLinear Algebra Premium
- Variance explained by a regressionMediumStatisticsLinear Algebra Premium
- When does the system fail to have a unique solution?MediumLinear Algebra Premium
- Why covariance matrices are PSDMediumStatisticsLinear Algebra Premium
- Inverse via Cayley–HamiltonHardLinear Algebra Premium
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Frequently asked questions
- What linear algebra do quant interviews test?
- Matrix multiplication and inverses, eigenvalues and eigenvectors, rank and null space, projections and least squares, and positive-(semi)definite matrices (which appear in covariance and optimisation).
- Which roles ask the most linear algebra?
- Quant-research and quant-developer roles, especially those touching statistics, machine learning, or optimisation. Pure-trading interviews ask it less often.
- How should I study linear algebra for interviews?
- Focus on intuition - what eigenvalues and eigenvectors mean and why projections give least-squares solutions - then drill problems so the mechanics are quick and accurate.