Thursday, February 23, 2006

Outer Product

Outer Product

The outer product is a way to build a higher rank tensor from those of lower rank. . One use of this is to combine two vectors to form a matrix as an outer product.
vec1 = {a,b,c}
vec2 = {x,y,z}

Inner product (dot product which would result in a scalar) = vec1 * vec2'

= {a,b,c} * { x} = ax + by + cz
{ y}
{ z}

Whereas the outerproduct is to increase the rank = vec1' * vec2

= {a} * { x, y, z} =

= ax, ay, az
bx, by, bz
cx, cy, cz

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