Bonus Day 2: Matrices & Transpose — Why Model 3 Math Needs This

Описание: This bonus lesson is all about matrices and transpose — not in an abstract math-class way, but in the exact way they show up inside PNNL Model 3 optimal start math.

In this video, we slow everything down and demystify what a matrix actually is. At its core, a matrix is just a list of vectors — rows of numbers that represent observations like Delta T, weather influence, and constants used in regression.

We then introduce transpose. No magic, no mystery. Transpose simply flips rows into columns so the dimensions line up correctly for math operations. This single idea unlocks the ability to compute XᵀX and Xᵀy, which are required for least-squares regression.

Why does this matter?
Because without transpose, Model 3 cannot exist. Full stop.

This lesson walks through:
• What a matrix represents in optimal start modeling
• What transpose really does (and why it exists)
• How transpose enables XᵀX and Xᵀy
• Why XᵀX is always square
• How to write your own transpose logic by hand
• Why this is doable even on resource-constrained BAS hardware

Everything here is built from scratch, using simple loops and logic — exactly the approach required when working inside a Niagara Program Object with no math libraries.

This is foundational material. Once transpose clicks, the rest of Model 3 regression math becomes much easier to reason about.

Lesson reference
https://github.com/bbartling/hvac-opt...)

Vibe Coding (Niagara Program Objects)
https://github.com/bbartling/niagara4...

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