Day 953: Linear Systems & Classical Complexity

Learning Objectives

• •**Formulate linear systems** in matrix form and understand their ubiquity in science
• •**Analyze classical direct methods** including Gaussian elimination and LU decomposition
• •**Explain iterative methods** such as conjugate gradient and their convergence properties
• •**Define the condition number** and its role in numerical stability and complexity
• •**Characterize sparse matrices** and their exploitation for efficient algorithms
• •**Establish the classical baseline** against which quantum speedups are measured

Today's Schedule (7 hours)