TITLE: What does this symbol $\otimes$ mean?
QUESTION [8 upvotes]: I came across the symbol $\otimes$ as below and I would like to know what this symbol $\otimes$ means:

$\text{.... the projection operator P is given by: }$
  $$P = I_nd - \nabla G^T(\nabla G \nabla G^T)^{-1} \nabla G= I_{nd} - I_d \otimes uu^T,$$ where $I_x$ denotes the identity matrix of size $x\times x$ and $\mathbf{u}$ is the unit vector , $\mathbf{u} = (1,1,1,\dots,1)/\sqrt{n})$ in $\mathbb{R}^n$

REPLY [10 votes]: In this context, $\otimes$ refers specifically to the Kronecker product.  In particular, we have
$$
I_d \otimes B 
= \overbrace{B \oplus B \oplus \dots \oplus B}^d
= \text{diag}(\overbrace{B,B, \dots, B}^d)\\
= \pmatrix{B\\&B\\&&\ddots\\&&&B}
$$