A matrix can do something surprisingly dramatic. It can collapse an entire dimension into nothing. The null space captures every direction that is completely eliminated, making it one of the most fundamental ideas in linear algebra, geometry, and countless areas of physics.
@business Proto Labs just posted its best earnings in 7 years and raised guidance. Injection molding's back, and data center + defense customers are the new growth story. $PRLB
this Stanford framework is f*cking insane
the entire hedge fund secret just got compressed into a 17 page PDF.
Stanford released the complete Hidden Markov Model framework that quants at firms like Jane Street and Two Sigma are known to run, and put it out for free.
the crazy part is this isn't a summary, it's the actual mechanics behind models these desks guard internally.
most people think this stuff stays locked behind institutional walls.
this one hands you the framework directly.
bookmark and read before someone takes it down.
Lump sum future value is FV = PV(1 + r)ⁿ, present value PV = FV/(1 + r)ⁿ. Annuity future value FVA = P[(1 + r)ⁿ − 1]/r, present PVA = P[1 − (1 + r)⁻ⁿ]/r. Perpetuity PVP = P/r, growing PVGP = P/(r − g). Doubling time DP = 72/r. Luca Pacioli wrote the rule of 72 in 1494, and Martín de Azpilcueta shaped the time value idea in the 1500s.
Quantum physics did not begin with strange experiments. It began with strange mathematics.
Ideas like superposition, entanglement, uncertainty, tunneling, and complex amplitudes looked impossible when they were first written on paper. Today, they explain how nature works at its smallest scales and power technologies from quantum computing to modern electronics.
The universe has always followed these rules. We just needed the mathematics to see them.
@mathemetica Solid summary of the classic CNN pipeline conv+ReLU building an edge→texture→part→object hierarchy, pooling downsampling, FC layer outputting class probabilities. That part's accurate, though "four rounds" is illustrative, not a fixed rule
(depth varies a lot by model)