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Equation 3 · Part 7 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Starting index or lower bound: i

Ij=∑iVi GijI_j = \sum_i V_i\, G_{ij}
ii

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

The multiplication step follows directly from two textbook circuit laws. Apply a voltage ViV_i simultaneously to each row i, representing the i-th component of an input vector. By Ohm’s law, the cell at row i and column j draws a current ViV_i times its conductance GiG_ij. By Kirchhoff’s current law, every current flowing into a given column sums automatically on that column’s wire, so the total current collected at the…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.