LIN-21

Trace 2×2

Matrix trace.

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GoverningTrace 2×2

Governing equation

\\mathrm{tr}=a+d

$a \in \left[-20, 20\right]$

where

a: a (—)
d: d (—)
tr: Trace 2×2 (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\\mathrm{tr}=a+d

$a \in \left[-20, 20\right]$

$a = -20$ $tr = -16$

Along the curve

②

Domain of the variable — blue

a_{\min} = -20,\quad a_{\max} = 20

$a \in \left[-20, 20\right]$

$a = -20$ $a = -20$

Along the curve

③

Response curve — green

\\mathrm{tr}=a+d

$a \in \left[-20, 20\right]$

$a = -20$ $tr = -16$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}tr}{\mathrm{d}a}

$a \in \left[-20, 20\right]$

$a = -19.75$ $tr^{\prime} = 1$

Along the curve

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-21 — Trace 2×2) is the form associated with Trace 2×2. Working symbols: $a$ , $d$ $\rightarrow$ $tr$ . Matrix trace. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

tr

from

a

d

in Linear algebra via

\\mathrm{tr}=a+d

Matrix trace. 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

a = 3.000\,\mathrm{—}

d = 4.000\,\mathrm{—}

, the governing relation

\\mathrm{tr}=a+d

yields

tr = 7.000\,\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

a a3 —d d4 —

Outputs

Trace 2×2 tr7.000 —

Reading speed

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Narration of this film

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

Matrix trace. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube