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Equation 45 · Part 1 · The Bend an Elevator Cannot Fake

Symbol phi_i

ϕi=ϕj\phi_i = \phi_j
ϕi\phi_i

What this part means

phiii_i is part of the quantity the equation computes from the expression on the right.

Its job in the formula

phiii_i is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…reverse. The null space of B has dimension equal to the number of connected components of the network graph; for a connected network it is exactly one-dimensional, spanned by the all-ones vector, because Bϕ\phi = 0 forces ϕi\phi_i = ϕj\phi_j across every edge and connectivity propagates that equality to every node. By rank–nullity, a connected tree — with exactly |V|-1 edges for |V| nodes — has an incidence matrix of full row rank, meaning that for any data whatsoever a ϕ\phi exists reproducing it exactly. A tree, in…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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