(Steps Shown) The Gram-Schmidt process. Let x_1,x_2,... be a sequence of linearly independent vectors in an inner product space. Define vectors inductively
Question: The Gram-Schmidt process. Let \({{x}_{1}},{{x}_{2}},...\) be a sequence of linearly independent vectors in an inner product space. Define vectors inductively as follows
\[{{e}_{1}}=\frac{{{x}_{1}}}{||{{x}_{1}}||}\]Show that \(({{e}_{n}})_{n=1}^{\infty }\) is an orthonormal sequence having the same closed linear span as the xj’s.
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