7.3-01 Sum and product of eigenvalues

Sum and product of eigenvalues

Use trace and determinant as independent checks on spectral calculations. Count repeated eigenvalues correctly, work with conjugate pairs and compare proposed spectra against both invariants.

What you will practise

• Recover trace from a spectrum
• Recover determinant from eigenvalues
• Include algebraic multiplicities
• Detect inconsistent spectral claims

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review basic eigenvalues and complex-number multiplication. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

The later questions recover missing information and reject candidates that satisfy only one invariant. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.