Meetup summary

2025-08-01 - Linear algebra basics - part 1

Linear algebra basics

Agenda:

Today will be the first part of however many sessions we need to get through the linear algebra prerequisites for probability. I’ll try to keep the sessions short and focused (in contrast to past ones).

  • Definitions and notation for:
    • Scalar
    • Vector
    • Matrix
  • Matrix products:
    • Scalar-matrix
    • Matrix-vector
    • Matrix-matrix (this is the only one that’s actually “interesting”)
      • Dot product can be interpreted as a special case of the matrix-matrix product of a 1×n1 \times n matrix with a n×1n \times 1 matrix. This is a different view than the “projection” view we started with last time.
    • Hadamard product (not particularly interesting, but it’s useful to recognize the notation because it is used in a few places)
  • Fundamental matrix product properties:
    • Associative
    • Distributive (over addition)
    • Not commutative
  • Other matrix operations:
    • Inverse (and product expansion)
    • Transposition (and product expansion)
    • Hermitian transposition (conjugate transposition)
  • Geometric interpretation of matrix-vector product
  • Preview of matrix determinants (won’t drill into details but will give broad strokes for what we want out of this operation).

Notes:

We got through the agenda including the geometric and algebraic interpretations of matrix multiplication. However, we did not have a chance to motivate or discuss determinants at all. This is where we’ll pick up next time. The linear algebra basics post contains most of the interesting things we covered today. Note that we discussed the notion of a matrix inverse and some high level properties, but not how to compute one, existence criteria, etc. Since this is closely associated with determinants (and both benefit strongly from a good geometric understanding), we’ll cover those together.

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