- #1
Prez Cannady
- 21
- 2
Given two probability distributions ##p \in R^{m}_{+}## and ##q \in R^{n}_{+}## (the "+" subscript simply indicates non-negative elements), this paper (page 4) writes down the tensor product as
$$p \otimes q := \begin{pmatrix}
p(1)q(1) \\
p(1)q(2) \\
\vdots \\
p(1)q(n) \\
\vdots \\
p(m)q(n)
\end{pmatrix}, $$
yet I expected to see
$$p \otimes q := \begin{pmatrix}
p(1)q(1) && p(1)q(2) && \cdots && p(1)q(n-1) && p(1)q(n) \\
p(2)q(1) && \ddots && && && p(2)q(n) \\
\vdots && && \ddots && && \vdots \\
p(m-1)q(1) && && && \ddots && p(m-1)q(n) \\
p(m)q(1) && p(m)q(2) && \cdots && p(m)q(n-1) && p(m)q(n)
\end{pmatrix}, $$
Am I missing something?
$$p \otimes q := \begin{pmatrix}
p(1)q(1) \\
p(1)q(2) \\
\vdots \\
p(1)q(n) \\
\vdots \\
p(m)q(n)
\end{pmatrix}, $$
yet I expected to see
$$p \otimes q := \begin{pmatrix}
p(1)q(1) && p(1)q(2) && \cdots && p(1)q(n-1) && p(1)q(n) \\
p(2)q(1) && \ddots && && && p(2)q(n) \\
\vdots && && \ddots && && \vdots \\
p(m-1)q(1) && && && \ddots && p(m-1)q(n) \\
p(m)q(1) && p(m)q(2) && \cdots && p(m)q(n-1) && p(m)q(n)
\end{pmatrix}, $$
Am I missing something?