Multi-Dimensional Arrays

You can declare arrays with as many dimensions as you need, even in excess of 20, although you will probably not have more than 3 or 4 maximum.
Multi Dimensional arrays can have up to 60 dimensions.
It is very unusual to use more than 2 or 3 dimensions.
When using 2-dimensional arrays always have columns and the rows, (ie (1,1) (1,2) (1,3) etc).
In a multi-dimensional array can you have vArrayName(1, 2, 1 ) When is it 2 dimensional ???

Rectangular Arrays - These are really 2 dimensional. The number of rows is identical to the number of columns.
Jagged Arrays - These are not really 2 dimensional and represent a 1 dimensional array of 1 dimensional arrays. Each element in the main array can hold an array of varying length.

Fixed Arrays

A multi dimensional fixed array is declared using the Dim statement.

Dim aCellValues(1 To 10, 1 To 100) As String 

This is a two dimensional array whose first index ranges from 1 to 10 and whose second index ranges from 1 to 100.

aCellValues(2,3) = "some text" 

Dynamic Arrays

A multi dimensional dynamic array must be declared on two lines

Dim aNumbers() As Integer 
ReDim aNumbers(1 to 10, 1 to 100) 

You can use the ReDim statement to change both the number of dimensions and the size of each dimension.
Only the upper bound of the last dimension in a multi-dimensional array can be changed.
A run-time error will occur if you try to change any other dimension.

Dim sCellValues(1 To 50, 1 To 10) As String 

ReDim aCellValues(1 To 50, 1 To 20) 
ReDim aCellValues(1 To 50, 1 To 20) As String 

Array Function

For more details refer to the ARRAY Function page.
You can also define and initialise multi-dimensional arrays

Dim vArray As Variant 
   vArray = Array( Array("one"), Array("Two"), Array("three"), Array("four") ) 

Limitations

A big disadvantage to using a multi dimensional array is that all the dimensions must contain the same data type.
User Defined Types can combine multiple data types into a single data type.
You can use a user defined type instead when you need to store values with different data types.

Matrices

Two dimensional arrays
Rectangular blocks of cells are called arrays or matrices

Adding

Add corresponding entries

Multiplying

Excel - MMULT

Inverse

Excel - MINVERSE

Excel Functions

TRANSPOSE
MDETERM

Preserving Values

You can only reduce the last dimension.
If you use the Preserve keyword, then you cannot change the number of dimensions.
If you use the Preserve keyword, then you are only able to resize the last dimension.

Dim aCellValues_Reduced(1 To 4, 1 To 100) 

ReDim Preserve aCellValues_Reduced(1 To 4, 1 To 50)