empty []

General [ ] properties

Empty brackets [] represent the empty matrix. Its general properties are now described.

1. It has only two dimensions. Any dimension > #2 is automatically squeezed:

   --> e = ones(1,2,0,2); size(e)
    ans  =
      0.   0.
   
   --> e == []
    ans  =
     T
   

2. It is always of real decimal type. There is no empty matrix of integer types (int8, uint8, int16, uint16, int32, uint32, int64, uint64), nor of string type, etc:

   --> type(uint8([]))  // not of type 8 (encoded integers)
    ans  =
      1.
   
   --> a = [1 2 ; 3 4] + %i;
   --> a(1,:) = []
    a  =
      3. + i     4. + i
   
   --> a(1,:) = [], isreal(a)
    a  =
       []
    ans  =
     T
   
   --> t = "abcd efg", type(t)
    t  =
    abcd efg
   
    ans  =
      10.
   
   --> t(1) = [], type(t)
    t  =
       []
   
    ans  =
      1.
   

3. However, it is distinct from the sparse empty matrix:

   --> se = sparse([])
    se  =
   (  0,  0) zero sparse matrix
   
   --> size(se)
    ans  =
      0.   0.
   
   --> se == []
    ans  =
     F
   

4. It is also distinct from all empty heterogeneous containers list(), struct() or cell() :

   --> L = list()
    L  =
        ()
   --> L == []
    ans  =
     F
   
   --> s = struct()
    s  =
   0x0 struct array with no fields.
   --> s == []
    ans  =
     F
   
   --> c = cell()
    c  =
      {}
   --> c == []
    ans  =
     F
   

[ ] as operand or input argument

1. As operand of usual predefined non-boolean operators, [] sets the result to []. All the following operations yield []:

   Unary operators
   []', [].', -[], ~[]
   Binary numerical operators
   addition:	[] + [1 2], [1 2] + []
   subtraction:	[] - [1 2], [1 2] - []
   division:	[]/[1 2], []./[1 2], [1 2]/[], [1 2]./[]
   left division:	[]\[1 2], [].\[1 2], [1 2]\[], [1 2].\[]
   multiplication:	[]*[1 2], [].*[1 2], [1 2]*[], [1 2].*[]
   kronecker:	[].*.[1 2], [1 2].*.[]
   power:	[]^[1 2], [].^[1 2], [1 2]^[], [1 2].^[]
   Inequality comparisons
   greater:	[]>[1 2], []>=[1 2], [1 2]>[], [1 2]>=[]
   less:	[]<[1 2], []<=[1 2], [1 2]<[], [1 2]<=[]

2. As operand of boolean binary operators, [] is equivalent to %T:

   Binary numerical operators
   or:	[] | [%T %F], [%T %F] | []	→	[%T %T]
   and:	[] & [%T %F], [%T %F] & []	→	[%T %F]

   But, noticeably:

   • or([]) is %F.

   • As the condition of any if or while statement, [] is %F:

     --> if []
     -->     r = "[] is %T as any if condition";
     --> else
     -->     r = "[] is %F as any if condition";
     --> end
     --> r
      r  =
      [] is %F as any if condition
     

3. In concatenations, [] is simply ignored: [A,[]] == [[],A] == [A ; []] == [[] ; A] == A

4. In text concatenations, +[] yields []: []+["a" "bc"] == ["a" "bc"]+[] == []

5. As special input matrix of linear algebra or common functions, the answer depends on the considered function. It is documented in the page dedicated to each function. Examples:

   det([]) 1 rank([]) 0 trace([]) 0 norm([]) 0 cond([]) 0 rcond([]) Inf

   diag([]) [] tril([]) [] triu([]) [] min([]) [] max([]) [] sign([]) [] clean([]) [] svd([]) []

   cumprod([]) [] cumsum([]) [] sum([]) 0 prod([]) 1 mean([]) Nan median([]) Nan stdev([]) Nan mad([]) Nan variance([]) Nan

6. As general input argument of functions, [] is often used to choose the default value of an input argument (to somewhat skip it, to avoid providing an actual explicit value). However, this is not a strict rule.

Assigning [ ] to delete ranges in arrays