Linear Algebra and Statistics

  • Use of vector and matrix notation, especially with multivariate statistics.
  • Solutions to least squares and weighted least squares, such as for linear regression.
  • Estimates of mean and variance of data matrices.
  • The covariance matrix that plays a key role in multinomial Gaussian distributions.
  • Principal component analysis for data reduction that draws many of these elements together.

Vector Spaces

  • An operation called vector addition that takes two vectors v, w ∈ V , and produces a third vector, written v + w ∈ V .
  • An operation called scalar multiplication that takes a scalar c ∈ F and a vector v ∈ V , and produces a new vector, written cv ∈ V . which satisfy the following conditions (called axioms).
  1. Associativity of vector addition: (u + v) + w = u + (v + w) for all u, v, w ∈ V .





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