# The notation $\otimes$ (Tensor product) [duplicate]

Related to the question Riemannian manifolds isometry, could anyone be able to explain to me what the notation $\otimes$? Some examples were given in the question : $dx\otimes dx+dy\otimes dy = \frac12(dz\otimes d\bar z + d\bar z\otimes dz) = |dz|^2$ or $dw \otimes d\bar{w}$.

Clarification : I think my question is different of What does this symbol $\otimes$ mean?, because I would like some details on a specific example.

• It denotes tensor product. – Michael Albanese Jul 26 '16 at 2:30

To understand tensor products from a linear algebra/module theory perspective I like Dummit and Foote's exposition. Formally the equality you have above comes from the parametrization $z= x+iy$, $\bar{z} = x -iy$, and billinearity of the tensor product.