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Can Gram–Schmidt process be used to orthonormalize a finite set of linearly independent vectors in a space with any nondegenerate sesquilinear form / symmetric bilinear form not necessarily positive definite?

For example in R^2 define

[tex]\langle a, b\rangle = - a_1\times a_1 + a_2\times a_2[/tex]

From [tex]\{v_1, v_2\}[/tex] to [tex]\{e_1, e_2\}[/tex], assume v's are not null.

[tex]e_1 = \frac{v_1}{|v_1|}[/tex]

where [tex]|v_1| = \sqrt{|\langle v_1, v_1\rangle|}[/tex]

[tex]t_2 = v_2 - \frac{\langle v_1, v_2\rangle}{\langle v_1, v_1\rangle}v_1[/tex]

[tex]e_2 = \frac{t_2}{|t_2|}[/tex]

It looks like it can be generalized to R^n without any problem.

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# Gram–Schmidt process

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