the.com/identity matrix

means A square matrix with 1s down the main diagonal and 0s everywhere else, which leaves any matrix or vector unchanged when multiplied by it.

from 'Matrix' comes from the Latin word for 'womb,' stemming from an earlier sense of a structure that generates or holds other things in place — a 19th-century mathematician adopted it for grids of numbers because a matrix could 'give birth to' other matrices via operations like determinants. 'Identity' traces back to Latin 'idem,' meaning 'the same,' via the medieval term 'identitas.' So the name is literally descriptive: this is the matrix that, under multiplication, hands back the same thing you started with — mathematics borrowing a word for sameness to name the ultimate do-nothing operator.