matrices and vectors

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Last updated 9:50 AM on 10/6/26

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1

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kronecker delta $\text{δ}_{ij}$

1 for i=j and 0 otherwise

2

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Levi-Civita ε_ijk

1 if ijk=123,231,312

0 for repeated index

-1 if ijk=321,213,132

3

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linear operator

Ô(f.g)=Ôf + Ôg

Ô(af) = aÔf

4

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linear vector space

rule for vector sum and scalar multiplication: |V>+|W>, a|V>

closure

distributive multiplication in vector and scalars

associative scalar multiplication

distributive scalar multiplication

associative addition

null vector |0>

inverse

5

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linearly independent

sum(a_i|i> = |0> is only true for all a_i=0