# 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 .

# MATRIX TRANSFORMATIONS

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