http://wiki.newmars.com/index.php?action=history&feed=atom&title=Basis_vector 2026-05-19T04:49:02Z Revision history for this page on the wiki MediaWiki 1.29.1 http://wiki.newmars.com/index.php?title=Basis_vector&diff=53&oldid=prev 2009-01-21T11:02:24Z

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Josh Cryer http://wiki.newmars.com/index.php?title=Basis_vector&diff=52&oldid=prev 2009-01-20T08:02:11Z

<p>Reverted edit of DelraCrova, changed back to last version by C M Edwards</p> <p><b>New page</b></p><div>A basis vector for a vector space is a set of linearly independent [[vector]]s where every [[object]] in the vector space can be described as a linear combinination of the basis vectors. For instance any [[position vector]] in a three-dimensional coordinate system with axis x, y and z can be described as a weighted sum of a vector of unit length in the x-axis, unit length in the y-axis and unit length in the z axis. In this example the weights in the weighted sum are the x, y and z coordinate of the point which is described by the position vector.<br /> <br /> There are 3 equivalent three-dimensional systems of basis vectors, popular for use in the physical sciences: <br /> <br /> * [[Cartesian Coordinates]], which are defined by projection relative to three intersecting [[orthogonal]] axes (axes at right angles to one another) whose common intersection forms an origin point. <br /> <br /> * [[Spherical Coordinates]], which are defined by radius and angle relative to a 3 dimensional [[polar]] [[reference frame]] with a fixed origin point. <br /> <br /> * [[Cylindrical Coordinates]], which are defined by projection relative to a central axis with a fixed origin point and by radius and angle within an orthogonal 2-dimensional polar reference frame defined relative to that central axis.<br /> <br /> Other three-dimensional systems of basis vectors can be defined as needed. Systems of basis vectors are typically selected on the basis of what is most convenient and/or elegant for the computation method employed. <br /> <br /> ==External Links==<br /> <br /> Definition of a basis vector from [[http://mathworld.wolfram.com/VectorBasis.html mathworld]].</div>

Josh Cryer