LIN-29

Hadamard 2×2

Entrywise product of the (1,1) pair.

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GoverningHadamard 2×2

Governing equation

A\\circ B

$a \in \left[-10, 10\right]$

where

a: a (—)
b: b (—)
p: Hadamard 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

A\\circ B

$a \in \left[-10, 10\right]$

$a = -10$ $p = -30$

Along the curve

②

Domain of the variable — blue

a_{\min} = -10,\quad a_{\max} = 10

$a \in \left[-10, 10\right]$

$a = -10$ $a = -10$

Along the curve

③

Response curve — green

A\\circ B

$a \in \left[-10, 10\right]$

$a = -10$ $p = -30$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}p}{\mathrm{d}a}

$a \in \left[-10, 10\right]$

$a = -9.874$ $p^{\prime} = 3$

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-29 — Hadamard 2×2) is the form associated with Hadamard 2×2. Working symbols: $a$ , $b$ $\rightarrow$ $p$ . Entrywise product of the (1,1) pair. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

p

from

a

b

in Linear algebra via

A\\circ B

Entrywise product of the (1,1) pair. 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 = 2.000\,\mathrm{—}

b = 3.000\,\mathrm{—}

, the governing relation

A\\circ B

yields

p = 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

a a2 —b b3 —

Outputs

Hadamard 2×2 p6.000 —

Reading speed

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Narration of this film

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

Entrywise product of the (1,1) pair. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube