Lets say $A, B$ and $C$ are invertible, linearly independent $d\times d$ matrices. Then is $A^{\otimes n} + B^{\otimes n} + C^{\otimes n}$ invertible for $n\gg d$ ? Thanks
invertibility of sums of tensor products of invertible matrices?
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linear-algebra
matrices
lie-groups
tensor-products
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1Seems it is not, in general. The counter example being $I^{\otimes n} + Z^{\otimes n} $ ($Z$ is the sigma-z matrix). It has eigen values of the form $1+(-1)^n$ which can be zero. – 2017-01-13