Matrices Represent Linear Mappings
See why transformed basis vectors become matrix columns, reconstruct a mapping from basis responses, and avoid row-versus-column mistakes in model weights.
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3articleswith this tag.
Dimension Counts Independent Directions
Separate the number of embedding coordinates from the number of samples, and learn why a matrix shape alone cannot tell you how many independent directions its vectors span.
A Basis Gives AI Vectors a Reversible Coordinate System
Test whether vectors form a basis, calculate coordinates in a new frame, and see how a linear model keeps the same score after a coordinated change.