Vandermonde matrix is widely used in many fields, e.g. Fast Fourier Transform.
Does this matrix always have inverse matrix?
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Assuming the points you use to construct it are all distinct, yes. – Sort of Damocles Jul 07 '18 at 03:19
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Maybe you should have a look at this question and the answers given there. – sharding4 Jul 07 '18 at 03:23
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If the roots are all distinct, and the degree of the roots is equal to the number of roots -1 then yes. Otherwise, you can reason about pseudoinverse and so on. In general, even if it is a tall matrix, if the roots are all distinct, you can say it has full rank. – yes Jun 16 '22 at 16:51