all function B = all(A < 0.5,3)

This is straight forward to me:

A = [0.53 0.67 0.01 0.38 0.07 0.42 0.69] 

A = 1×7

0.5300 0.6700 0.0100 0.3800 0.0700 0.4200 0.6900

B = all(A < 0.5,1)

B = 1×7 logical array
   0   0   1   1   1   1   0

this also makes sense -

A = [0.53 0.67 0.01; 0.38 0.07 0.42 ] 

A = 2×3

0.5300 0.6700 0.0100 0.3800 0.0700 0.4200

B = all(A < 0.5,2)

B = 2×1 logical array
   0
   1

But why does this yield the same result?

A = [0.53 0.67 0.01 1.1; 0.38 0.07 0.42 0.01] 

A = 2×4

0.5300 0.6700 0.0100 1.1000 0.3800 0.0700 0.4200 0.0100

B = all(A < 0.5,3)

B = 2×4 logical array
   0   0   1   0
   1   1   1   1

OR

B = all(A < 0.5,4)

B = 2×4 logical array
   0   0   1   0
   1   1   1   1

[Stephen23]

"But why does this yield the same result?"

Consider the sub-arrays (i.e. vectors) along each of the specified dimensions: what values do they have in them? Remember that all arrays implicitly have infnite trailing singleton dimensions: the fact that each of those vectors for dimensions 3 and 4 happen to have one element in them is irrelevent, ALL applies its algorithm on that one element. It might help to revise this: https://www.mathworks.com/help/matlab/math/multidimensional-arrays.html

Lets consider the top left corner of your data:

A = [0.53 0.67 0.01 0.38 0.07 0.42 0.69];
A(1,1,:) % top left, all elements along 3rd dimension

ans = 0.5300

A(1,1,1,:) % top left page1, all elements along 4th dimension

ans = 0.5300

You can repeat this yourself for every other element in your matrix.

Question: what do you expect the result to be? Why?

Answer 1

[the cyclist]

The reason is that all MATLAB arrays have implied singleton dimension beyond the 2nd dimension, if they have not been actually specified.

A = [0.53 0.67 0.01 1.1;
     0.38 0.07 0.42 0.01];

size(A,47)

ans = 1

Answer 2

[Torsten]

But why does this yield the same result?

Because A has only 2 dimensions, not 3 or 4. Thus "all" operates on all elements separately in both cases.

[VBBV]

Thus "all" operates on all elements separately in both cases., Yes, thats correct. But if one uses 'all' option it would do only once.

A = [0.53 0.67 0.01 1.1; 0.38 0.07 0.42 0.01] 

A = 2×4

0.5300 0.6700 0.0100 1.1000 0.3800 0.0700 0.4200 0.0100

B = all(A < 0.5,'all')

B = logical
   0

B = all(A < 0.5,3)

B = 2×4 logical array
   0   0   1   0
   1   1   1   1

B = all(A < 0.5,4)

B = 2×4 logical array
   0   0   1   0
   1   1   1   1