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The calculator functions by applying the Gram Schmidt orthogonalization process on a set of linearly independent vectors or on the columns of a matrix to get the orthonormal basis of the space that is spanned by the vectors.
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14 Απρ 2019 · Use the Gram-Schmidt process to find the orthonormal basis for the row space of the matrix $A$.
The Gram-Schmidt process is a very useful method to convert a set of linearly independent vectors into a set of orthogonal (or even orthonormal) vectors, in this case we want to find an orthogonal basis $\{v_i\}$ in terms of the basis $\{u_i\}$.
In this lecture we finish introducing orthogonality. Using an orthonormal ba sis or a matrix with orthonormal columns makes calculations much easier. The Gram-Schmidt process starts with any basis and produces an orthonormal ba sis that spans the same space as the original basis. 1 if i = j.
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