i need to prove that if tr(A^2)=0(adsbygoogle = window.adsbygoogle || []).push({});

then A=0

we have a multiplication of 2 the same simmetrical matrices

why there multiplication is this sum formula

[iTEX]

A*A=\sum_{k=1}^{n}a_{ik}a_{kj}

[/iTEX]

i know that wjen we multiply two matrices then in our result matrix

each aij member is dot product of i row and j column.

dont understand the above formula.

and i dont understand how they got the following formula:

then when we calculate the trace (the sum of the diagonal members)

we get

[TEX]

tr(A^{2})=\sum_{i=1}^{n}A_{ii}^{2}=\sum_{i=1}^{n}(\sum_{i=1}^{n}a_{ik}a_{ki})

[/TEX]

and because the matrix is simmetric then the trace is zero

why?

i need to prove that if tr(A^2)=0

then A=0

can you explain the sigma work in order to prove it?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Trace prove question

**Physics Forums | Science Articles, Homework Help, Discussion**