The Hadamard Edge: Why Entrywise Multiplication Powers AI

We unpack the Hadamard (Schur) product: simple A ∘ B, equal-shaped matrices multiplied entrywise. It’s commutative and, crucially, why PSD matrices stay PSD thanks to the Schur product theorem—giving a stability guarantee for big systems. See how this tiny operation shows up in image masking, JPEG-like processing, and the gate-driven memory of LSTMs/GRUs, and why it's a foundation of fast AI runtimes (NumPy, MATLAB). Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.Sponsored by Embersilk LLC