leftimage for poohprod.ru

Dot Product (also known as Inner or Scalar Product)



The dot product is a scalar number and so it is also known as the scalar or inner product. In a real vector space, the scalar product between two vectors
vectors for dot product
is computed in the following way:

dot product

Besides, there is another way to define the inner product, if you know the angle between the two vectors:

other definition for dot product

We can conclude that if the inner product of two vectors is zero, the vectors are orthogonal.

In Matlab, the appropriate built-in function to determine the inner product is 'dot(u,v)'.

For example, let's say that we have vectors u and v, where

u = [1 0] and v = [2 2]. We can plot them easily with the 'compass' function in Matlab, like this:



x = [1 2]
y = [0 2]
compass(x,y)



x represents the horizontal coordinates for each vector, and y represents their vertical coordinates. The instruction 'compass(x,y)' draws a graph that displays the vectors with components (x, y) as arrows going out from the origin, and in this case it produces:

compass drawing for dot product


We can see that the angle between the two vectors is 45 degrees; then, we can calculate the scalar product in three different ways (in Matlab code):



a = u * v'
b = norm(u, 2) * norm(v, 2) * cos(pi/4)
c = dot(u, v)



Code that produces these results:
a = 2
b = 2.0000
c = 2

Note that the angle has to be expressed in radians, and that the instruction 'norm(vector, 2)' calculates the Euclidian norm of a vector (there are more types of norms for vectors, but we are not going to discuss them here).


From 'Dot Product' to home

From 'Dot Product' to 'Matlab Examples'

Top

Angle between vectors

Cross Product




footer for dot product page



























Related pages


fibonacci number calculatoramerican standard code for information interchange tablemaclaurin expansion calculatorsecond degree polynomial regressionhow do you calculate square feet from inchesamortisation table mortgagemaclaurin series for sin xhow to find the salvage valuec program for curve fittinghypotenuse of a triangle calculatorcalculate nominal interest ratematlab matrix determinantpolyval in matlabammortization tablesmatlab gui exampletextscanlog function in matlabdirac impulse functionascii chart tablepythagorean theorum calculatordirac impulseascii code for letterscombinations calctower of hanoi codesolved problems on mesh analysissolve definite integrals onlinematlab tutorialif statements in matlabimpulse response of rc circuitpiecewise defined function examplebcd to gray codematlab curvefitcosine expansioninverse t distribution calculatorhexadecimal binary tablecharging rc circuitresistor number code calculatorbisection method matlab code exampleconvert cartesian to cylindricalcalculating loan payment formuladirac impulseohms law piematlab gui textboxconverting ascii to chardeclaring functions in matlabascii value of azplot line graph matlabexamples of fibonacci numbersregression in matlabmatlab programming for beginnersascii code binary tablematlab sum matrixfour band resistor color codematlab fit functionhypotenuse leg calculatorhow to create histogram in matlabpolar histogrammatlab guide examplesintegrals in matlabanimation matlabdefinite calculatoramerican standard code for information interchange tableequation solver matlabonline double integral calculatorohm law calcbinary to decimal examplesbilinear interpolation codedefinite calculatorconverting binary to hexhow to learn matlab quicklyintegral calculator with boundsmatlab tutorial for beginnerspascal triangle in c using arrayoctal basepascal's triangle solver