How to get rid of nested matrices

Question

If I type into Mathematica

TensorProduct[IdentityMatrix[2],IdentityMatrix[2]]

It gives me a result that has nested matrices. How do I turn that into a normal matrix without any nesting? Thanks

$\begingroup$ Look at Flatten, Join, et al. ... $\endgroup$
– ciao
Jul 2, 2014 at 2:32 — ciao, Jul 2, 2014 at 2:32

halirutan · Accepted Answer · 2014-07-02 02:32:23Z

11

Depends on what dimension your final matrix is supposed to have. When I should make a guess, I would say you want this

TensorProduct[IdentityMatrix[2], IdentityMatrix[2]] // ArrayFlatten

answered Jul 2, 2014 at 2:32

halirutan♦

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kglr · Accepted Answer · 2014-07-02 14:14:52Z

4

An alternative approach is to use KroneckerProduct which does not require flattening.

From the docs on TensorProduct:

The KroneckerProduct of matrices is equivalent to the flattening of their TensorProduct to another matrix.

That is, for any two matrices m1 and m2

KroneckerProduct[m1, m2] == ArrayFlatten[TensorProduct[m1, m2]]
(* True *)

So,

m1 = IdentityMatrix[2];
KroneckerProduct[m1, m1] == ArrayFlatten[TensorProduct[m1, m1]]
(* True *)

answered Jul 2, 2014 at 14:14

kglr

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$\begingroup$ Excellent. I've been looking to define such a function. Is there a convenient symbol for it like with the Tensor Product: esc t* esc ? $\endgroup$
– Travis Bemrose
Jul 12, 2016 at 20:10
1

$\begingroup$ @Travis, maybe you can define an input alias such as CurrentValue[$FrontEndSession, {InputAliases, "KrP"}] = RowBox[{"KroneckerProduct[", "\[SelectionPlaceholder]", ",", "\[Placeholder]", "]"}] and use it as Esc KrP Esc to get a template with placeholders. Or, define CirclePlus = KroneckerProduct and us it as matrix1 Esc c+ Esc matrix2. $\endgroup$
– kglr
Jul 12, 2016 at 20:33

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2 Answers 2