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| − | A place where nobody dared to go
| + | {{move|quadratic form}} |
| − | The love that we came to know
| + | '''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. |
| − | They call it Xanadu
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| | | | |
| − | And now
| + | A quadratic form ''q('''x''')'' can be written as: |
| − | Open your eyes and see
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| − | What we have made is real
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| − | We are in Xanadu
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| | | | |
| − | A million lights are dancing | + | :''q('''x''')'' = '''''x'''''(''A'' '''''x''''') |
| − | And there you are
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| − | A shooting star
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| − | An everlasting world
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| − | And you're here with me
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| − | Eternally
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| | | | |
| − | Xanadu, Xanadu,
| + | 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. |
| − | (now we are here) | |
| − | In Xanadu
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| − | Xanadu, Xanadu,
| |
| − | (now we are here) | |
| − | In Xanadu
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| | | | |
| − | Xanadu, your neon lights will shine
| + | [[Category:linear algebra]] |
| − | For you, Xanadu
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| − | | |
| − | The love
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| − | The echoes of long ago
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| − | You needed the world to know
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| − | They are in Xanadu
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| − | | |
| − | The dream
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| − | That came through a million years
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| − | That lived on through all the tears
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| − | It came to Xanadu
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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
| |
| − | Eternally
| |
| − | | |
| − | Xanadu, Xanadu,
| |
| − | (now we are here)
| |
| − | In Xanadu
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| − | Xanadu, Xanadu,
| |
| − | (now we are here)
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| − | In Xanadu
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| − | | |
| − | Now that I'm here
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| − | Now that you're near in Xanadu
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| − | Now that I'm here
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| − | Now that you're near in Xanadu
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| − | Xanadu...
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