From the course: Machine Learning Foundations: Linear Algebra

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Gram–Schmidt process

Gram–Schmidt process

From the course: Machine Learning Foundations: Linear Algebra

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Gram–Schmidt process

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- Let's understand the concept of Gram-Schmidt process that we can use to transform any basis to orthogonal basis. It is much simpler to perform calculations in orthogonal basis. We'll look at the process in general before heading into the first example. Our matrix contains a few columns. In our case, imagine we have a matrix with five columns. When we apply Gram-Schmidt to the first column, our first column stays the same. Then we take the second column and orthogonalize it relative to the first column. We apply the same process to the third column relative to the second column and to the first column. It means we subtract two parts. Part of the column that is parallel to the column two and part of the column that is parallel to the column one. We repeat the process until the last column. At the end, we get a matrix in which all the columns are orthogonal, but this matrix is not an orthogonal matrix due to the fact not…

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