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4 minor equation edit

If $A$ is an element of $\mathbb{R}^n \otimes\mathbb{R}^n \otimes\mathbb{R}^n$, then define its injective tensor norm to be $$\|A\|~_{\rm \|A\|_{\rm inj} := \max_{x,y,z\in \mathbb{R}^n, \|x\|=\|y\|=\|z\|=1} |\langle A, x\otimes y\otimes z\rangle|.$$ Here the norm on vectors is the usual Euclidean norm.

I have two questions.

1. Does this norm change if x,y,z can be taken to arbitrary complex unit vectors?
2. What if $A$ is symmetric under exchange of the first two positions? That is,
$\langle A, x\otimes y\otimes z\rangle = \langle A, y\otimes x\otimes z\rangle$ for all $x,y,z$.
3 Corrected order of factors in 2nd question

If $A$ is an element of $\mathbb{R}^n \otimes\mathbb{R}^n \otimes\mathbb{R}^n$, then define its injective tensor norm to be $$\|A\|~_{\rm inj} := \max_{x,y,z\in \mathbb{R}^n, \|x\|=\|y\|=\|z\|=1} |\langle A, x\otimes y\otimes z\rangle|.$$ Here the norm on vectors is the usual Euclidean norm.

I have two questions.

1. Does this norm change if x,y,z can be taken to arbitrary complex unit vectors?
2. What if $A$ is symmetric under exchange of the first two positions? That is,
$\langle A, x\otimes y\otimes z\rangle = \langle A, x\otimes y\otimes x\otimes z\rangle$ for all $x,y,z$.
2 added tag and fixed latex

If $A$ is an element of $\mathbb{R}^n \otimes\mathbb{R}^n \otimes\mathbb{R}^n$, then define its injective tensor norm to be $$\|A\|~{\rm \|A\|~_{\rm inj} := \max{x,y,z\in max_{x,y,z\in \mathbb{R}^n, \|x\|=\|y\|=\|z\|=1} |\langle A, x\otimes y\otimes z\rangle|.$$ Here the norm on vectors is the usual Euclidean norm.

I have two questions.

1. Does this norm change if x,y,z can be taken to arbitrary complex unit vectors?
2. What if $A$ is symmetric under exchange of the first two positions? That is,
$\langle A, x\otimes y\otimes z\rangle = \langle A, x\otimes y\otimes z\rangle$ for all $x,y,z$.
1