Linear independence
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
One subtraction clears a direction
A basis is a set of directions to measure along, and most bases are awkward because the directions get in each other's way. Removing one shadow at a time turns any basis into one where every coordinate is a shadow and nothing interferes.
The nearest point of a flat thing
More equations than unknowns almost never have a solution. Asking instead for the point of a plane nearest to where the answer should have been turns an unanswerable question into a shadow, and the shadow is what a line of best fit is.
How often a table of random signs is flat
Fill a square table with random plus and minus signs and ask whether its determinant is nought. For four rows the answer is yes two times in three. The chance then falls, and since 2020 it has been known to fall at exactly the rate of the dullest accident, two rows or columns equal or opposite. The conjecture is that this accident is, in the end, the whole story. Every size a computer can reach says otherwise, and the theory says the computer has not gone far enough.
Named alongside it
The objects these essays reach for when they reach for this one.
ApproximationBasisDot productGram schmidtInner productLeast squaresOrthogonalityOrthonormal basisProjectionResidualSubspaceCauchy schwarz