Weird behavior when changing parts of matrix

Question

I have this matrix:

mat = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 
    17, 18, 19, 20}, {21, 22, 23, 24, 25}};

and here are its second row and second column:

{mat[[2]], mat[[All, 2]]}
(* {{6, 7, 8, 9, 10}, {2, 7, 12, 17, 22}} *)

When I tried to change its second column to all zeros, this method works:

mat = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 
    17, 18, 19, 20}, {21, 22, 23, 24, 25}};
mat[[All, 2]] = 0;
mat // MatrixForm

But using the method to change the second row, the entire row become a big zero:

mat = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 
    17, 18, 19, 20}, {21, 22, 23, 24, 25}};
mat[[2]] = 0;
mat // MatrixForm

---

My question is:

1) Why would the replacement of a row versus a column in a matrix different?

2) Why would setting the list of all column elements to zero automatically set each of them to zero? Setting a list to a single number doesn't seem to work in isolation:

{a, b, c} = 0

Answer 1

Actually, I think the reason it works like this is because Mathematica lists can be anything, so it assumed you want the second element of this list of lists to be 0. So if you want all elements of that second sublist to be 0, you have to specify it just like you did for the column.

mat = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 
    17, 18, 19, 20}, {21, 22, 23, 24, 25}};

Then:

mat[[2, All]] = 0

OR

mat[[2, ;;]] = 0

mat // MatrixForm

Answer 2

This is simply the logical outcome of Mathematica treating an array as an ordinary expression tree.

Your array isn't really an array at all, but merely a collection of List expressions inside another List expression, all of which happen to be the same length. And like any other ordinary expression in an assignment you can change a part using Set:

expr = foo[bar, baz];

expr[[2]] = 0;

expr

foo[bar, 0]

While Mathematica can store a true array in the case of packed arrays these are handled in such a way as to make operations behave identically to the same operation on the equivalent ordinary expression. (There are exception but I digress.)

If you wish to zero all values within a row you can specially address all parts of the row as RunnyKine did, with e.g. a[[2, All]] = 0;, or you can simply multiply the row by 0, since Times is a Listable operation:

a = Partition[Range@9, 3];

a[[2]] *= 0;

a

{{1, 2, 3}, {0, 0, 0}, {7, 8, 9}}