Programming 
Computing with Multidimensional Arrays
Many of the MATLAB computational and mathematical functions accept multidimensional arrays as arguments. These functions operate on specific dimensions of multidimensional arrays; that is, they operate on individual elements, on vectors, or on matrices.
Operating on Vectors
Functions that operate on vectors, like
sum
, mean
, and so on, by default typically work on the first nonsingleton dimension of a multidimensional array. Most of these functions optionally let you specify a particular dimension on which to operate. There are exceptions, however. For example, the cross
function, which finds the cross product of two vectors, works on the first nonsingleton dimension having length 3.
Operating ElementbyElement
MATLAB functions that operate elementbyelement on twodimensional arrays, like the trigonometric and exponential functions in the elfun
directory, work in exactly the same way for multidimensional cases. For example, the sin
function returns an array the same size as the function's input argument. Each element of the output array is the sine of the corresponding element of the input array.
Similarly, the arithmetic, logical, and relational operators all work with corresponding elements of multidimensional arrays that are the same size in every dimension. If one operand is a scalar and one an array, the operator applies the scalar to each element of the array.
Operating on Planes and Matrices
Functions that operate on planes or matrices, such as the linear algebra and matrix functions in the matfun
directory, do not accept multidimensional arrays as arguments. That is, you cannot use the functions in the matfun
directory, or the array operators *, ^
, \
, or /
, with multidimensional arguments. Supplying multidimensional arguments or operands in these cases results in an error.
You can use indexing to apply a matrix function or operator to matrices within a multidimensional array. For example, create a threedimensional array A
:
Applying the eig
function to the entire multidimensional array results in an error:
You can, however, apply eig
to planes within the array. For example, use colon notation to index just one page (in this case, the second) of the array:
Note
In the first case, subscripts are not colons; you must use squeeze to avoid an error. For example, eig(A(2,:,:)) results in an error because the size of the input is [1 3 3] . The expression eig(squeeze(A(2,:,:))) , however, passes a valid twodimensional matrix to eig .

Permuting Array Dimensions  Organizing Data in Multidimensional Arrays 
© 19942005 The MathWorks, Inc.