I came across this equation in a book on financial econometrics.
If $R_t$ is an $N \times 1$ matrix, $B$ is an $N \times K$ matrix, $R_{kt}$ is a $K \times 1$ matrix, $\gamma_0$ is a scalar
and $\iota$'s dimension is given as 'a conforming vector of ones'
Can I write the following?
\begin{align} R_t = \iota \gamma_0 + B(R_{kt} - \iota \gamma_0) \end{align}
If so, what is the dimension of $\iota$?
Since $R_t$ is an $N \times 1$ column vector the first term $\iota \gamma_0$ must be $N \times 1$ implying that the dimension of $\iota$ must be $N \times 1$ but since B is $N \times K$ the term $(R_{Kt} - \iota \gamma_0)$ must be $K \times 1$, implying the dimension of $\iota$ is $K \times 1$.
Can $\iota$ be both $N \times 1$ and $K \times 1$ in the same equation?
The original text seems to use the same notation to denote two different objects.
You might like to introduce a subscript to denote the length of the vector to make things clearer.
\begin{align} R_t = \iota_N \gamma_0 + B(R_{kt} - \iota_K \gamma_0) \end{align}