Hi guys,
I've been working on a problem that involves 2 components,
(a) The inner Product of two tensor's both of rank 2 (i.e. Matrices) and
(b) The inner Product (or Tensor Product - not sure of the terminology) of a rank 2 tensor with a rank 3 tensor.
Found a solution via googling for (a) thankfully, being that if A, B are both rank 2 tensors then,
<A,B> = Tr(AB^T)
Which if I'm not mistaken is the form for all tensor products of equal rank (again could be wrong).
My issue lies with (b); I understand this is a help forum and not a step by step solution page, but I was wonder what the procedure (or starting point) for dealing with a Rank 2 tensor A and a Rank 3 tensor B, i.e.
<A,B> = ? I know that it will be a tensor of rank 3 using the rank formula (r1 + r2 - 2); but have been lost trying to follow the work I've found on the net.
Any help would be greatly appreciated.
Regards,
David
edit - I'm not sure if this makes things easier, but in this case
A = uv^T , B = wx^Tz^T
where u,v,w,x,z are Real n x 1 vectors.
I've been working on a problem that involves 2 components,
(a) The inner Product of two tensor's both of rank 2 (i.e. Matrices) and
(b) The inner Product (or Tensor Product - not sure of the terminology) of a rank 2 tensor with a rank 3 tensor.
Found a solution via googling for (a) thankfully, being that if A, B are both rank 2 tensors then,
<A,B> = Tr(AB^T)
Which if I'm not mistaken is the form for all tensor products of equal rank (again could be wrong).
My issue lies with (b); I understand this is a help forum and not a step by step solution page, but I was wonder what the procedure (or starting point) for dealing with a Rank 2 tensor A and a Rank 3 tensor B, i.e.
<A,B> = ? I know that it will be a tensor of rank 3 using the rank formula (r1 + r2 - 2); but have been lost trying to follow the work I've found on the net.
Any help would be greatly appreciated.
Regards,
David
edit - I'm not sure if this makes things easier, but in this case
A = uv^T , B = wx^Tz^T
where u,v,w,x,z are Real n x 1 vectors.
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