Linear Operators Part 1

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In this video we introduce the concept of a linear operator and demonstrate how a linear operator acting on a Finite-dimensional Vector space can be represented by a matrix.
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I like how you have not used confusing symbols in equations and left it to the readers to decode what the symbols mean. This now makes sense.
Usually you do not know that two sigmas is just summation with two indices unless you are a mathematician. It is concise to write equations with confusing symbols, but also makes it difficult for the reader to understand. Even those who know what the symbols mean take time to understand what exactly is the meaning of the symbols and what the equation is saying.

avinashsuresh
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One of the best linear algebra videos Ive seen in a while, amazing :D

Barba_
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Nice clarification. Thanks much for sharing.

lcfrod
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The range and the domain is not at all same. The thing is that the dimension of the domain and codomain would be same and this too only when the inverse exists. So for a linear operator the range and domain arent same.

paulimmanuel
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I'm confused: Wolfram says a linear operator acts on functions. And that an operator is "mapping between two function spaces"?

Also, the second paragraph of the Wikipedia page titled Linear Map says, in one convention, "a linear operator allows V and W to differ". Why the ambiguity / inconsistency?

bentupper