LIN-22

Frobenius 2×2

Entrywise 2-norm.

Reading speed

GoverningFrobenius 2×2

Governing equation

\\|A\\|_F=\\sqrt{a^2+b^2+c^2+d^2}

where

a: a (—)
b: b (—)
c: c (—)
d: d (—)
F: Frobenius 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-22 — Frobenius 2×2) is the form associated with Frobenius 2×2. Working symbols: $a$ , $b$ , $c$ , $d$ $\rightarrow$ $F$ . Entrywise 2-norm. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

F

from

a

b

c

d

in Linear algebra via

\\|A\\|_F=\\sqrt{a^2+b^2+c^2+d^2}

Entrywise 2-norm. 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 = 1.000\,\mathrm{—}

b = 2.000\,\mathrm{—}

c = 0.000\,\mathrm{—}

d = 4.000\,\mathrm{—}

, the governing relation

\\|A\\|_F=\\sqrt{a^2+b^2+c^2+d^2}

yields

F = 4.583\,\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 a1 —b b2 —c c0 —d d4 —

Outputs

Frobenius 2×2 F4.583 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

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

Entrywise 2-norm. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube