What is the difference between [v' 1] and [v', 1]?

I come across these two notations and still cannot distinguish them.

v' is the transpose of v. The first notation [v' 1] will be transpose of v' with column of 1 at the end.

Is [v', 1] related to matrix indexing? Please help.

Answer 1

[KSSV]

v = rand(3,1) ;
[v' 1]

ans = 1×4

0.5957 0.0098 0.4734 1.0000

[v',1]

ans = 1×4

0.5957 0.0098 0.4734 1.0000

That is nothing but vector v is increased by one element at the end and the value is 1.

Answer 2

[Walter Roberson]

v = ((1:3) -(2:4)*1i).'

v = 
   1.0000 - 2.0000i
   2.0000 - 3.0000i
   3.0000 - 4.0000i

[v' 1]

ans = 
   1.0000 + 2.0000i   2.0000 + 3.0000i   3.0000 + 4.0000i   1.0000 + 0.0000i

[v', 1]

ans = 
   1.0000 + 2.0000i   2.0000 + 3.0000i   3.0000 + 4.0000i   1.0000 + 0.0000i

You can see that even for complex numbers, [v' 1] and [v', 1] produce the same results. This is not an accident.

The difference between [v' 1] and [v', 1] is that the version with the comma reduces the risk of values accidentally being treated as subtraction:

[v' -1]

ans = 
   1.0000 + 2.0000i   2.0000 + 3.0000i   3.0000 + 4.0000i  -1.0000 + 0.0000i

[v', 1]

ans = 
   1.0000 + 2.0000i   2.0000 + 3.0000i   3.0000 + 4.0000i   1.0000 + 0.0000i

[v'  - 1]

ans = 
   0.0000 + 2.0000i   1.0000 + 3.0000i   2.0000 + 4.0000i

[v', - 1]

ans = 
   1.0000 + 2.0000i   2.0000 + 3.0000i   3.0000 + 4.0000i  -1.0000 + 0.0000i

Notice that the [v' - 1] form was treated as subtraction of 1, but [v' -1] and [v', -1] and [v', - 1] forms treated the -1 or - 1 as a negative 1 rather than a subtraction.

The rule is:

If the last thing you saw was a delimiter or a delimiter followed by whitespace, then + and - following are the "unary plus" and "unary minus" operators, no matter whether they are followed by whitespace or not.

If the last thing you saw was an expression without delimiter, or whitespace after an expression without delimiter, then + followed by whitespace is addition, and - followed by whitespace is subtraction, but + followed without whitespace is unary plus, and - followed without whitespace is unary minus.

 %   U  U    S   A
  [1 +1 -1 1 - 1 + 2]

ans = 1×4

1 1 -1 2

U here indicating unary operator, S indicating subtraction, A indicating addition. Compare to

  [1, +1, -1, 1, - 1, + 2]

ans = 1×6

1 1 -1 1 -1 2

So the comma help prevent accidental interpretation as subtraction or addition