Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

question about inner product formula

Status
Not open for further replies.

ran_out

Newbie level 6
Newbie level 6
Joined
Nov 24, 2003
Messages
13
Helped
0
Reputation
0
Reaction score
1
Trophy points
1,281
Activity points
111
hi all,

i have a question regarding the relation:

(x_transpose)y= norm_x* norm_y * cos(α)

where x, y are vectors and α is the angle between them.

from law of cosines u get:

cos(α) = (norm_ x^2 + norm y ^2 - norm_(x-y)^2) / (2*norm_x*norm_y)

right?

but how do you get the relation:

norm_ x^2 + norm y ^2 - norm_(x-y)^2 = 2*(x_transpose)y

which is needed to get the final result

(x_transpose)y = norm_x* norm_y * cos(α)

Thanx for help
 

According to the definition of the inner product,
norm_(x-y)^2=(x-y,x-y)
=norm_x^2-xy-yx+norm_y^2
=norm_x^2 + norm_y^2 - 2*(x_transpose)y

Therefore,
norm_ x^2 + norm y ^2 - norm_(x-y)^2
=2*(x_transpose)y.
 

huge thanx for that
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top