# Column or row of a matrix?

The question is so simple, but I cannot find the answer.

Is $M_i$ (usually) the $i^{\text{th}}$ column of matrix $M$? Or the $i^{\text{th}}$ row?

Since $M_{ij}$ is the $j^{\text{th}}$ element of the $i^{\text{th}}$ row, I would say $M_i$ is the row. On the other hand we usually work with column vectors and it is therefore unusual to take a row from a matrix and it would be illogical to have a simple notation for something that is used less often.

If $M_i$ is the $i^{\text{th}}$ row, how would I get the $i^{\text{th}}$ column? Surely not $(M^T)_i$!

• Could you give the context, perhaps cite the sentence in which $M_i$ occurs? – Mussé Redi May 31 '14 at 14:25
• I don't know of a standard notation for either the rows or columns, except maybe $M_{i*}$ and $M_{*j}$. – Hew Wolff May 31 '14 at 14:25
• So $M_i$ is unusual notation? – Angelorf May 31 '14 at 14:26
• I would tend toward $M_i$ as the i-th row. "Unfortunately" in Python pandas when we ask df[0] it means the column label matching 0 instead of 0th row or 0th column (which is okay in Data Science-speak, but can be weird coming from math). – Hendy Irawan Feb 16 '18 at 8:10