Hi,

I almost finished the linear algebra course, by now I’m W4 - eigenvalues. Throughout the course there is a lot of emphasis on the importance of characterizing a matrix through the calculation of its determinant to understand whether it is singular or non-singular but, honestly, I cannot grasp the real meaning of this information when applying the operations between matrices or the algorithms.

How should knowing whether a matrix is Singular help a Data Scientist or Machine Learning Engineer?

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In practice, generally it doesn’t.

Using determinants is important in linear algebra, as a general concept. For example, when you form a series of equations into a matrix, as a solution method, the determinant tells you in advance whether a unique solution will exist.

But that’s not how machine learning works. Remember, M4ML is essentially a math course with some tidbits of machine learning thrown in.

In machine learning, the matrix of the training examples is typically huge, and you’re going to find a model that fits it as well as possible. Under-determined systems (where you have more features than you have examples) are obvious without calculating determinants.

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