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Gram-Schmidt orthogonalization and Legendre Polynomials using the Wolfram Language
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In this video tutorial I show you how to orthogonalize a basis for a vector space of polynomials. It might seems a strange thought, but yes, polynomials that are orthogonal to each other can be created.
In the tutorial I explain the concept of the inner product between two polynomials and use the Gram-Schmidt process to create the orthogonal set of polynomials.
While it is an easy task, I use the Wolfram Language in this video to make life (and understanding) even easier. Code along if you have access to the Wolfram Language or search Google for "Wolfram Programming Lab" and sign up for a free account. You can then code along right in your favorite browser.
At the end of the tutorial, when we have our set of orthogonal polynomials, I also discuss how they are slightly modified to give us the Legendre polynomials.
In this video tutorial I show you how to orthogonalize a basis for a vector space of polynomials. It might seems a strange thought, but yes, polynomials that are orthogonal to each other can be created.
In the tutorial I explain the concept of the inner product between two polynomials and use the Gram-Schmidt process to create the orthogonal set of polynomials.
While it is an easy task, I use the Wolfram Language in this video to make life (and understanding) even easier. Code along if you have access to the Wolfram Language or search Google for "Wolfram Programming Lab" and sign up for a free account. You can then code along right in your favorite browser.
At the end of the tutorial, when we have our set of orthogonal polynomials, I also discuss how they are slightly modified to give us the Legendre polynomials.
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