Linear Algebra for Quantitative Finance

What Will You Learn?

• Master the Foundations of Vector Spaces: Understand vector spaces, subspaces, linear combinations, dependence/independence, and how these concepts apply to data structures in finance.
• Solve and Analyze Systems of Linear Equations: Apply Gaussian and Gauss-Jordan elimination, understand consistency, and interpret the existence and uniqueness of solutions — crucial for portfolio construction and regression modeling.
• Manipulate and Interpret Matrices: Perform matrix operations (addition, multiplication, inverse, transpose) and understand how linear transformations relate to real-world financial problems.
• Compute and Apply Determinants: Analyze invertibility and system solvability using determinant properties, and solve linear systems with Cramer’s Rule when applicable.
• Explore Eigenvalues, Eigenvectors, and Diagonalization: Grasp their significance in financial modeling, especially in Principal Component Analysis (PCA) used for factor risk modeling and yield curve analysis.
• Bridge Theory with Quantitative Finance Applications: Solve real-world problems like yield curve decomposition and optimal asset allocation using core linear algebra techniques.