Extra Pure

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Last updated 3:09 PM on 6/15/26
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6 Terms

1
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Imaginary Roots of Auxiliary Equation (when in form angle: theta, magnitude: p)

un=pn(Acos ntheta + Bsin ntheta)

2
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Tests for Group

Associative

Closure

Identity

Inverse

3
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Subgroup Tests for Infinite Groups

Closure

Identity

Inverse

4
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Subgroup Tests for Finite Groups

Non empty
Closure - repeatedly applying will eventually produce identity

5
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Checks for Isomorphism

Same size

Identity maps

Same orders

Same special properties (Abelian, Cyclic)

6
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Diagonalising a Square Matrix

M= SAS-1

Where M is matrix

A is eigenvalue matrix

S is eigenvector matrix