Converting a Matrix into an Orthonormal Basis: Solving the Gram-Schmidt Problem

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To convert a 3x3 matrix A into an orthonormal basis using the Gram-Schmidt process, the first step involves applying the Gram-Schmidt algorithm to obtain orthonormal vectors. The second part of the task requires producing an upper triangular matrix B such that the product AB results in an orthogonal matrix. This indicates that the problem is related to QR factorization, where A can be decomposed into an orthogonal matrix Q and an upper triangular matrix R. Clarification is sought on how to effectively track the steps to achieve this upper triangular form. Understanding the relationship between the Gram-Schmidt process and QR factorization is crucial for solving the problem.
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So I need to use Gram Schmidt to convert a 3x3 matrix A into an orthonormal basis. This is straightforward enough. But then I need to 'keep track of your steps to produce an upper triangular matrix B so that AB is an orthogonal matrix.' I'm not sure what this second part entails. Is this a QR factorization problem?


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