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LIN-21

Trace 2×2

Matrix trace.

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GoverningTrace 2×2

Governing equation

mathrmtr=a+d\\mathrm{tr}=a+d

where

a
a (—)
d
d (—)
tr
Trace 2×2 (—)

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: aa, dd →\rightarrow trtr. Matrix trace. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute trtr from aa, dd in Linear algebra via mathrmtr=a+d\\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 —a = 3.000\,\mathrm{—}, d=4.000 —d = 4.000\,\mathrm{—}, the governing relation mathrmtr=a+d\\mathrm{tr}=a+d yields tr=7.000 —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.

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Inputs

Outputs

  • Trace 2×2 tr7.000 —
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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