# Hoffman Kunze - Definition of Row Reduced Echelon Matrix

I am unable to understand the 2nd definition of row-reduced echelon matrices in

• Kenneth Hoffman, Ray Kunze, Linear Algebra, 2nd edition 1971.

Attached is the image:

In part a) it says $$R_{ij} = 0$$ if $$j < k_i$$ which implies all entries in columns < $$k_i$$ will be zero. however I would have thought it should be$$R_{ij} = 0$$ if $$j < min(k_i)$$ or $$R_{ij} = 0$$ if $$j < k_1$$.

Also point b) is not clear because subscript of left side $$R_{ik_i}$$ and right side $$\delta_{ij}$$ are different. I mean I was expecting some constraint like $$j <= k_i$$.

Please help me understand the notation. Even though I am clear what a row reduced Echelon matrix is from the 1st definition but need to understand this notation as this is common across the book.

• Look more closely at condition (b). It’s a bit hard to read in your image, but the subscript is $k_j$, not $k_i$. – amd Apr 16 '19 at 18:56

It’s a bit hard to read in the image that you’ve uploaded, but the subscript in condition (b) is $$k_j$$, not $$k_i$$, i.e., the condition is really $$R_{ik_j}=\delta_{ij}, 1\le i\le r, 1\le j\le r$$. This, together with the other conditions, ensures that the only nonzero entry in column $$k_i$$ occurs in row $$i$$.