special matrix product

**Skalkaz** · January 18th 2009, 02:12 PM

Hi, I'm not native English, what is the name the following product. Let a n-column vector and b m-row vector, than c = a × b resultes a n-by-m-matrix:
c_ij = a_i * b_j.

**NonCommAlg** · January 18th 2009, 03:17 PM

Originally Posted by Skalkaz

Hi, I'm not native English, what is the name the following product. Let a n-column vector and b m-row vector, than c = a × b resultes a n-by-m-matrix:
c_ij = a_i * b_j.

i don't know if there's a name for this but what you've defined is simply this $\bold{c}=(\bold{ba})^T.$

**Skalkaz** · January 18th 2009, 03:37 PM

What does ba mean?
b and a are vector, and n <>= m.

This product is very usefull sometimes,for example:
the matrix of the tranformation r --> a(br) is
T = a × b
where a, b, r is spatial vector, and br is scalar product

**NonCommAlg** · January 18th 2009, 03:47 PM

$\bold{b}$ is an $m \times 1$ vector and $\bold{a}$ an $1 \times n.$ so $\bold{b}\bold{a}$ is an $m \times n$ matrix. clearly $(\bold{b}\bold{a})^T$ would be the matrix that you called $\bold{c}.$

**Skalkaz** · January 18th 2009, 04:08 PM

Oh, you are absolutly right.

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