TITLE: What is the name of the matrix that is created by a vector times its transpose.
QUESTION [6 upvotes]: I am looking for the name of the matrix created by the following operation:
$Z = z*z^T$
I know it should create a symmetric matrix with an element $Z_{ij} = z_{i}z_{j}$

REPLY [6 votes]: This is a special case of the tensor product of vectors known as outer product. It has some interesting properties, for example that the trace of the matrix is the square of the (Euclidean) norm of the vector. And as you point out it is always symmetric.