hello, I'm supposed to check if the matrix is square if not, disp a message. when i used [n,m]=size(A), if n~=m, disp, it seems to work; if i use [n,n]=size(A),

can you please tell me what's wrong in below and how to use [n,n]=size(A) properly? silly question but you can tell i'm new. Thansk a lot.

[n,n] = size(A);
disp('coefficient matrix A must be square')

Answer 1

[Walter Roberson]

[n,n] = size(A);

That means to assign the first output of size() to n, and then to assign the second output of size to n, overwriting the value that was just written.

It has the same effect as

[~,n] = size(A);

or as

[ThisVariableIsNotUsed, n] = size(A);
clear ThisVariableIsNotUsed

It does not in any way compare the two outputs of A.

... and you do not have any if statement, so unless the [n,n]=size(A) errors out, the disp() is always going to be run.

[Wesley Lei]

thank you so much, that makes perfect sense

Answer 2

[David Hill]

Has to be two different variable; otherwise you are overriding the first assignment. You can use a single variable, such as:

n=size(A);%will be an array
isequal(n(1),n(2))

[Wesley Lei]

thank you so much, i got it now

Answer 3

[Christophe]

After having defined the matrix A, I'd just type

A' - A

if MATLAB gives an error, it means that A isn't square : )

[Stephen23]

"if MATLAB gives an error, it means that A isn't square"

Lets check that now:

A = 0:5 % not square

A = 1×6

0 1 2 3 4 5

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A' - A % no error -> does not work.

ans = 6×6

0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 4 3 2 1 0 -1 5 4 3 2 1 0

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Rather than obfuscating the test behind some code that does not do what this answer incorrectly claims, the best** way to check if a matrix is square is to test its size.

** clearest, easiest to understand, easiest to maintain, probably quite efficient, etc.

[Christophe]

ok, so try A * A and it gives an error, or eig(A) and it gives an error

btw MATLAB should givre an error with A'-A, since you cannot subtract matrices with different dimensions, but ok

>> A'-A

ans =

0 -1 -2 -3 -4 -5

1 0 -1 -2 -3 -4

2 1 0 -1 -2 -3

3 2 1 0 -1 -2

4 3 2 1 0 -1

5 4 3 2 1 0

>> A*A

Error using *

Incorrect dimensions for matrix multiplication. Check that the number of columns in the

first matrix matches the number of rows in the second matrix. To operate on each

element of the matrix individually, use TIMES (.*) for elementwise multiplication.

Related documentation

>> eig(A)

Error using eig

Input matrix must be square.

[Steven Lord]

btw MATLAB should givre an error with A'-A, since you cannot subtract matrices with different dimensions, but ok

That has not been the case for several years. See this documentation page.

To forestall the questions/comments I expect you to post next based on previous feedback:

• No, this is not a bug.
• Yes, we know what mathematics says the rules are.
• This is a generalization of scalar expansion that has been part of MATLAB since Cleve's original Fortran version IIRC.
• No, there is no way to disable this behavior.
• We discussed internally whether we should define new operators to perform this expansion operation rather than changing the existing operators before we released it.
• Yes, I am certain this is not a bug.

To expand upon one of Stephen23's objection to your transpose-and-subtract or your eig approaches to telling if a matrix is square: if the matrix is large and square, and so the check succeeds, how long is it going to take to perform those calculations and how much memory is the resulting array (and any intermediate temporary variables created during the calculations) going to consume? Calling size (I would argue you should also ask ismatrix as well, to safeguard against a 3-d array with the right combinations of sizes) is going to create a few scalar values and it doesn't have to do much (or any) calculations in the process.

The 3-d concern:

A = rand(4, 2, 2);
[rows, colsSortOf] = size(A)

rows = 4

colsSortOf = 4

issquareSortOf = isequal(rows, colsSortOf)

issquareSortOf = logical
   1

This is documented behavior of the size function, BTW. From that documentation page:

• When dim is not specified and fewer than ndims(A) output arguments are listed, then all remaining dimension lengths are collapsed into the last argument in the list. For example, if A is a 3-D array with size [3 4 5], then [sz1,sz2] = size(A) returns sz1 = 3 and sz2 = 20.

I believe this behavior is from back when MATLAB first introduced N-dimensional arrays (for N > 2) in MATLAB 5.0 (I think. That was well before the start of my time at MathWorks.)