Linear Algebra · Linear algebra
Determinants
The determinant as the area (or volume) scaling factor of a transformation: the 2×2 and 3×3 formulas, sign and orientation, zero determinant means squashing and no inverse, det(AB) = det A · det B, and uses in eigenvalues and change of variables.
Step 1 of 6 · Overview30 min read ·
Key idea
Prereqs: Matrices as transformations; Matrix multiplication. Next: Solving linear systems; Eigenvectors & eigenvalues. Sources: 3Blue1Brown, *Essence of Linear Algebra* ch. 6; Strang, *Introduction to Linear Algebra* ch. 5.Next: 1. Meaning