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LIN-25

Parallelogram area

2-D cross magnitude.

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GoverningParallelogram area

Governing equation

A=∣uxvy−uyvx∣A=|u_x v_y-u_y v_x|

where

ux
ux (—)
uy
uy (—)
vx
vx (—)
vy
vy (—)
A
Parallelogram area (—)

Lecture brief

Historical brief

Determinants, eigenvalues, least squares and Cayley–Hamilton are the nineteenth-century matrix craft behind every coupled system. The sheets invert, project and diagonalise small n. This sheet (LIN-25 — Parallelogram area) is the form associated with Parallelogram area. Working symbols: uxux, uyuy, vxvx, vyvy →\rightarrow AA. 2-D cross magnitude. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute AA from uxux, uyuy, vxvx, vyvy in Linear algebra via A=∣uxvy−uyvx∣A=|u_x v_y-u_y v_x| 2-D cross magnitude. Use it when a real linear algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given ux=3.000 —ux = 3.000\,\mathrm{—}, uy=0.000 —uy = 0.000\,\mathrm{—}, vx=1.000 —vx = 1.000\,\mathrm{—}, vy=2.000 —vy = 2.000\,\mathrm{—}, the governing relation A=∣uxvy−uyvx∣A=|u_x v_y-u_y v_x| yields A=6.000 —A = 6.000\,\mathrm{—}. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Parallelogram area A6.000 —
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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

2-D cross magnitude. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube