What's the correct notation for a minimum of a row of a matrix?

Question

• $I=\{1,\cdots,m\}$ denote the indices of the rows of a matrix $A$
• Let $J=\{1,\cdots,n\}$ denote the indices of the columns of matrix $A$
• Let $x_{i,j}$ denote the value of the element $A[i,j]$

I need to use a notation to indicate the minimum value for each row. Is it correct if I do it like so? $$\min_{j\in J}(x_{i,j}) \ \ \ \ \ \ \ \forall i\in I$$

Answer 1

If I needed a vector of row-minima, I'd write $$ u_i = \min_{j\in J} x_{ij}, ~i = 1, \ldots, m. $$

In other words, almost exactly what you've written. In general, I like to denote the $ij$ element of a matrix $A$ by $a_{ij}$, so my real preferred answer would be $$ u_i = \min_{j\in J} a_{ij}, ~i = 1, \ldots, m. $$