Unit 15: A quick way to 2×2 eigenvalues
About this unit
For a 2×2 matrix the eigenvalues average to m, half the trace, and multiply to p, the determinant, so they are m ± √(m² − p).
By the end, you can: Find a 2×2 matrix's eigenvalues straight from its trace and determinant, and tell from m² − p whether they are real.
Modules
5 modulesLearn
- Two numbers you can read offArticle · A 2×2 matrix's eigenvalues add up to its trace and multiply to its determinant, so they are m ± √(m² − p) with m half the trace and p the determinant.Not started
- Eigenvalues in three linesWalkthrough · Find the eigenvalues of a matrix with a negative determinant using the mean and the product.Not started
- When the root goes negativeWalkthrough · Spot a matrix with no real eigenvalues from the sign of m² − p.Not started
- The shortcut on one cardReview · The mean–product formula, its checks, and what the sign under the root says.Not started