Maths · What a determinant measures
What does a determinant actually measure?
What you’ll see
A matrix is just four numbers. What does its determinant measure? Read each column as where an arrow lands. The first column moves the green arrow here, the second moves the red arrow there. Now let the whole grid follow them. The square they started with stretches into a parallelogram, and its area grows from one to exactly five. Every square on the grid grows five times. That's the determinant: a times d, minus b times c. Three times two, minus one times one, is five. And if the arrows line up, space is squashed flat. The determinant is zero.
