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2012-06-07 04:38:37 -0600 | commented answer | Calculating an Orthonormal Basis might take me a while to understand it fully, but great thanks! |

2012-06-07 04:37:59 -0600 | commented answer | Calculating an Orthonormal Basis wow, thanks! |

2012-06-07 01:31:35 -0600 | received badge | ● Editor (source) |

2012-06-07 01:31:06 -0600 | asked a question | Calculating an Orthonormal Basis Hi, I'm still quite inexperienced with Sage at the moment, so forgive me if this is a basic issue. I am trying to produce an orthonormal basis, I have created the orthogonal complement to my original basis by taking its left nullspace using kernel() I now want to use gram_schmidt() to produce a normalised version. I am unsure however what ring my input matrix should be over. QQbar won't work for me, but I am worried that the RDF result I get will not retain the linear independence that I need, as it says in the documentation for gram_schmidt() that under RDF, if I change the ring of this matrix to RDF, gram_schmidt() runs but the inexact entries of -0.0 and what is clearly 1/sqrt(2) are not so useful. Does anybody know where I've gone wrong here? Is there another more reliable method for computing an orthonormal basis that I could use? Thanks again for putting up with a newbie! best regards Brian |

2012-05-01 06:27:35 -0600 | received badge | ● Student (source) |

2012-05-01 01:10:57 -0600 | commented question | A question on symbolic Matrices - unexpected Decimals in algebraic entry fantastic! thanks! I cast the result of mag^2 to an int and got the results I was expecting, great stuff! This has allowed me to verify my calc against an example and I can use this as a basis for what I'm trying to build up. Many thanks! |

2012-05-01 00:22:55 -0600 | asked a question | A question on symbolic Matrices - unexpected Decimals in algebraic entry Firstly, I'd just like to say that I am starting out with Sage adn Python at the moment, really impressed by the power of Sage and its potential! I am coming at this from an engineering and C++ background, and am currently trying to look at an engineering problem using some matrix linear algebra. I am setting up a from of stiffness matrix and am trying to extract the symbolic eigenvalues and eigenvectors from this. The stiffness matrix below is generated through a few different matrix multiplication operations, based on node and connectivity matrices. Despite trying to define these as being "SR" rings, I seem to end up with entries like (b + 1.0g + 1.0s) rather than the (b + g + s) I was expecting. I suspect this is due to me not understanding rings properly and how to apply them. I have tried the explanations in the Sage documentation, can anybody recommend some further reading or tutorials on this, because it does seem to be a vital topic in getting to grips with Sage? I enclose my code below, in case anybody can spot a glaringly stupid thing that I've done... many thanks, Brian |

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