Equation 47 · Part 1 · The Bend an Elevator Cannot Fake
Symbol V
What this part means
V is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
V is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol V→Article meaning
The passage around this formula
What r is actually sensitive to follows from the same argument in 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 B = 0 forces = 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 exists reproducing it exactly. A tree, in other words, cannot fail to close, on any data, ever; it carries zero redundant edges and therefore zero capacity to…
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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