EE263 Autumn 2007-08 Stephen BoydLecture 20Some parting thoughts . . .• linear algebra• levels of understanding• what’s next?20–1Linear algebra• comes up in many practical contexts (EE, ME, CE, AA, OR, Econ, . . . )• nowadays is readily donecf. 10 yrs ago (when it was mostly talked about)• Matlab or equiv for fooling around• real codes (e.g., LAPACK) widely available• current level of linear algebra technology:– 500 – 1000 vbles: easy with general purpose codes– much more possible with special structure, special codes (e.g., sparse,convolution, banded, . . . )Some parting thoughts . . . 20–2Levels of understandingSimple, intuitive view:• 17 vbles, 17 eqns: usually has unique solution• 80 vbles, 60 eqns: 20 extra degrees of freedomPlatonic view:• singular, rank, range, nullspace, Jordan form, controllability• everything is precise & unambiguous• gives insight & deeper understanding• sometimes misleading in practiceSome parting thoughts . . . 20–3Quantitative view:• based on ideas like least-squares, SVD• gives numerical measures for ideas like singularity, rank, etc.• interpretation depends on (practical) context• very useful in practiceSome parting thoughts . . . 20–4• must have understanding at one level before moving to next• never forget which level you are operating inSome parting thoughts . . . 20–5What’s next?• EE363 — linear dynamical systems (08-09)• EE364a — convex optimization I (Win 07-08)• EE364b — convex optimization II (Spr 07-08)(plus lots of other EE, CS, ICME, MS&E, Stat, ME, AA courses on signalprocessing, control, graphics & vision, adaptive systems, machine learning,computational geometry, numerical linear algebra, . . . )Some parting thoughts . . .
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