LIN-34

Scaled identity det

Diagonal of λ.

Reading speed

GoverningScaled identity det

Governing equation

\\det(\\lambda I_n)=\\lambda^n

where

lam: lam (—)
n: n (—)
D: Scaled identity det (—)

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-34 — Scaled identity det) is the form associated with Scaled identity det. Working symbols: $lam$ , $n$ $\rightarrow$ $D$ . Diagonal of λ. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

D

from

lam

n

in Linear algebra via

\\det(\\lambda I_n)=\\lambda^n

Diagonal of λ. 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

lam = 2.000\,\mathrm{—}

n = 3.000\,\mathrm{—}

, the governing relation

\\det(\\lambda I_n)=\\lambda^n

yields

D = 8.000\,\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

lam lam2 —n n3 —

Outputs

Scaled identity det D8.000 —

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.

Diagonal of λ. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube