Mathmatical Notation

Once again GDNet comes up trumps.

Thanks anons

D.V.

Carpe Diem


Edited by - DeltaVee on January 11, 2002 9:02:20 AM

Anonymous Poster...You where rigth both times...

|A| in any dimension sums up the square of the axis, and then takes the squareroot of them, to get the magnitude...

However, in 1D, it just happens the sqrt(a^2) is allways positive, since squared non-imaginary numbers allways >= 0

A little advanced mathematical notation stuff to confuse you all. In higher math (e.g., graduate school level math), the bar |?| or (more appropriate) double bar ||?|| notation simply indicates that you should calculate a "norm" of the item inside. For example,

B = |A|

means B equals a "norm" of A. It just happens that when A and B are vectors the most common "norm" is the Euclidian norm, the length of the vector A, which is calculated using the familiar formula:

B = Euclidian norm of A = sqrt(A.x²+A.y²+A.z²)

The Euclidian norm is sometimes called the "2-norm". That is because we add the components of A to the "2" power (squared) and then take the 1 over 2 (1/2 or sqrt) root of that sum. There is another norm called the "1-norm" and it is simply:

B = 1-norm of A = abs(A.x) + abs(A.y) + abs(A.z)

where abs() is absolute value (or same as |?| of a scalar)

Its computed kind of the same way as the 2-norm. Add the absolute value of components of A raised to the "1" power, and then take the 1 over 1 (=1) root of that sum. The root doesn''t do anything and you''re just left with the sum.

The 1-norm is cheaper to calculate than the 2-norm, and in some areas of math and geometry it is useful. There are really a whole bunch of different norms that are sometimes useful. The Euclidian norm, 1-norm, and the infinity-norm are perhaps the most common.

When you''re dealing with norms in higher math, it is customary to put a subscript outside of the |?| to indicate exactly which norm is desired, for example:

B = |A|₂

Its also a bit more customary to use the double bars:

B = ||A||₂

So, just a little trivia for you, .

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Doesn''t the |whatever| mean modulus?