Back in March, we explained how to normalize column vectors with Excel. But, what about normalizing row vectors? This question is addressed in the current QA column of IRW. I think it might be useful sharing the answer with readers since many of these are students struggling with similar questions. So, here we go.

The following table emulates an Excel array consisting of three columns (A, B, and C) and six rows (1-6).

  A B C
1 1 2 3
2 4 5 6
3 7 8 9
4 0.27 0.53 0.80
5 0.46 0.57 0.68
6 0.50 0.57 0.65

Rows 1, 2, and 3 are row vectors. Rows 4, 5, and 6 are the corresponding normalized vectors, also known as unit vectors because their length is 1. To compute these, do as follows:

1. In cell A4, enter the formula =A1/(SQRT(SUMSQ($A1:$C1))). The result should be as given in this cell.

2. Copy this formula, select cells A5 and A6 and paste the formula in these.

 3. Finally, copy at once cells A4 through A6, select the remaining empty cells of the array, i.e., cells B4 through C6 and paste the formulas in these.