AMS 210 : Applied Linear Algebra

General Mathematical Principle for Multivariable Problems. Any problem involving several unknowns is normally solved by recasting the problem as a system of linear equations.

ModelsDeterministicProbabalistic
StaticEquilibrium Model
  • Leontief: x̅ = Ax̅ + b̅
  • DynamicEcological ModelMarkov Chain

    In Linear Programming (A.K.A. Linear Optimization), we optimize a linear objective function.

    MatrixCan Represent
    Transition Matrix
    ( ||·||s=1 )
    1. Markov Chain
    2. Filter: Linear Filtering smooths data by multiplying by a (usually Band) Transition Matrix. I.E. f ~ Σ <k,fᵢ>||k||₁ f̂ᵢ
    0-1 MatrixGraphs

    AA is a measure of the similarity between the columns of A.

    DeterminantInvertible
    = 0No
    ≠ 0Yes
    ~ 0Ill-conditioned

    λ ≤ ||·||

    A Partitioned Matrix has matrices as elements.