Index Notation Article Index for
Index 		Website Links For
Notation 		 

Information About

Index Notation
  CATEGORIES ABOUT INDEX NOTATION
   
mathematical notation
   
computer programming
   
APPAREL
BABY
BEAUTY
BOOKS
CAR TOYS
CELL PHONES
DVD'S
ELECTRONICS
GOURMET FOOD
GROCERIES
HEALTH & PERSONAL
HOME & GARDEN
JEWELRY
MUSIC
MUSIC INSTRUMENTS
OFFICE PRODUCTS
SOFTWARE
SPORTING GOODS
TOOLS & HARDWARE
TOYS
VIDEO GAMES
SHOPPING HOME
MORE SHOPPING...



It is quite common in some mathematical proofs to refer to the elements of an array using subscripts, and in some cases superscripts. The use of superscripts is frequently encountered in the theory of General Relativity . The following line states in effect that the each of the elements of a vector ''c'' are equal to the sum of the elements of vectors '''''a''''' and '''''b'''''
:\mathbf{c}_j = \mathbf{a}_j + \mathbf{b}_j

so
:\mathbf{c}_0 = \mathbf{a}_0 + \mathbf{b}_0
:\mathbf{c}_1 = \mathbf{a}_1 + \mathbf{b}_1
and so on.

See also: Summation Convention


In several programming languages, index notation is a way of addressing elements of an array. This method is used since it is closest to how it is implemented in Assembly Language whereby the first element of the address is used as a base and a multiple (the index) of the element size is used to address inside the array.

For example, a block of memory at location 0x3000 is the Base Address , and if we are storing 4 byte integers, then elements in this block of memory are at memory locations 0x3000, 0x3004, 0x3008, 0x300c, ..., 0x3000 + 4''n''. In general, the memory location of the ''i''th element with Base Address ''b'' and element size ''s'' is ''b''+''is''.


C IMPLEMENTATION DETAILS



Multidimensional arrays

Things become more interesting when we consider arrays with more than one index, for example, a two-dimensional table. We can either do two things:
  • make the two-dimensional array one-dimensional

  • consider a one-dimensional array of each element in a one-dimensional array


  • (---(base + i) + j).



Example

This function multiplies two 3x3 floating point matrices together.

void mult3x3f(float result const float A[ const float B[ [3])
{
int i, j, k;
for (i = 0; i < 3; ++i) {
for (j = 0; j < 3; ++j) {
result {Link without Title} {Link without Title} = 0;
for (k = 0; k < 3; ++k)
  • B[k [j];

    • }

}
}


IN OTHER LANGUAGES

In other programming languages such as Pascal, indices may start at 1, so indexing in a block of memory can be changed to fit a start-at-1 addressing scheme by a simple linear transformation - in this scheme, the memory location of the ''i''th element with Base Address ''b'' and element size ''s'' is ''b''+(''i''-1)''s''.