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I am tutoring a mixed class of (mostly) engineers and physicists and I am trying to get across how important the concept of a vector space is - that its not just some abstract problem that only pure mathematicians need to worry about.

Its easy to highlight the need for linear algebra for physicists - Quantum Mechanics is entirely based on it. I am finding it harder to justify to engineers where they will use vector spaces - I know its important for time domain (state space) control theory and you describe stresses in materials using tensors.

Can anyone think of other applications of vector spaces for engineers ?

Cheers,

Thrillhouse