Reviewed stability definition, and covered the special (stronger) condition of backwards stability, which is true of many algorithms and often not too hard to prove. Showed that floating-point summation of n numbers is backwards stable.

When quantifying errors, a central concept is a norm. Defined norms (as in lecture 3 of Trefethen), gave examples of Lp norms (usually p = 1, 2, or ∞).

More norms: weighted norms, Frobenius norm, and induced matrix norms. Bounded induced square-matrix norm in terms of matrix eigenvalues (we will give a more precise bound later in terms of SVDs). Showed that unitary matrices preserve L₂ norms and induced norms, and also the L₂ Frobenius matrix norm.

Equivalence of norms. Sketched proof that any two norms are equivalent up to a constant bound, and that this means that stability in one norm implies stability in all norms. The proof involves: (i) showing that all norms are continuous; (ii) showing that we can reduce the problem of showing any norm is equivalent to L₂ on the unit circle; and (iii) a result from real analysis: a continuous function on a closed/bounded set achieves its maximum and minimum.