Difference between revisions of "Quadratic form"

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(confusing notation, mixing matrix notation and vector notation)
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{{move|quadratic form}}
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A place where nobody dared to go
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'''Quadratic forms''' are functions expressed as multivariable equations in [[linear algebra]] that have only combined power of two.  When represented by [[matrices]], they have a geometric significance as a shift or transformation in coordinates.
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The love that we came to know
 +
They call it Xanadu
  
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A quadratic form ''q('''x''')'' can be written as:
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And now
 +
Open your eyes and see
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What we have made is real
 +
We are in Xanadu
  
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:''q('''x''')'' = '''''x'''''(''A'' '''''x''''')
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A million lights are dancing
 +
And there you are
 +
A shooting star
 +
An everlasting world
 +
And you're here with me
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Eternally
  
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where '''''y''''' = ''A'' '''''x''''' is the vector resulting from multiplying a matrix and a vector (a [[linear transformation]]) and '''''x''''' ('''''y''''') is the [[scalar product]] of vectors.
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Xanadu, Xanadu,
 +
(now we are here)  
 +
In Xanadu
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
  
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[[Category:linear algebra]]
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Xanadu, your neon lights will shine
 +
For you, Xanadu
 +
 
 +
The love
 +
The echoes of long ago
 +
You needed the world to know
 +
They are in Xanadu
 +
 
 +
The dream
 +
That came through a million years
 +
That lived on through all the tears
 +
It came to Xanadu
 +
 
 +
A million lights are dancing
 +
And there you are
 +
A shooting star
 +
An everlasting world
 +
And you're here with me
 +
Eternally
 +
 
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
 +
Xanadu, Xanadu,
 +
(now we are here)
 +
In Xanadu
 +
 
 +
Now that I'm here
 +
Now that you're near in Xanadu
 +
Now that I'm here
 +
Now that you're near in Xanadu
 +
Xanadu...

Revision as of 12:59, August 11, 2010

A place where nobody dared to go The love that we came to know They call it Xanadu

And now Open your eyes and see What we have made is real We are in Xanadu

A million lights are dancing And there you are A shooting star An everlasting world And you're here with me Eternally

Xanadu, Xanadu, (now we are here) In Xanadu Xanadu, Xanadu, (now we are here) In Xanadu

Xanadu, your neon lights will shine For you, Xanadu

The love The echoes of long ago You needed the world to know They are in Xanadu

The dream That came through a million years That lived on through all the tears It came to Xanadu

A million lights are dancing And there you are A shooting star An everlasting world And you're here with me Eternally

Xanadu, Xanadu, (now we are here) In Xanadu Xanadu, Xanadu, (now we are here) In Xanadu

Now that I'm here Now that you're near in Xanadu Now that I'm here Now that you're near in Xanadu Xanadu...

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