Linear Algebra Comment: Reusing the Same Letter in Different Expressions

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[@MathTheBeautiful]

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[@3koningen]

Yes that's it. Wow, I see the difference now. These deeper thoughts make me so enthusiastic about math again. I want to study it all and hoop you will be our guide for a long time and for many subjects. Than you.

[@jeffreagan2001]

Is it correct to say that the left hand side of the expression is a noun (collection of vectors) while the right hand side is an adjective (mathematical expression which is a description of the null space)?

[@MathTheBeautiful]

I believe that's accurate.

[@CstriderNNS]

so wouldn't it be more accurate to wright the expression of the null space as the null set........ { N : a[x] +b[y] } ?

[@CstriderNNS]

lol i didnt read below

[@BrianKCatlin]

Wouldn't it be more correct - or at least less ambiguous - to put curly braces around the right side of the equation, denoting it as a set rather than an equality?

[@MathTheBeautiful]

Yes, that would be more correct and I used to do that with my class. But then I realized that it would also be unnecessarily more formal so I started using the less formal notation. (Also, you can think of both alpha and beta as sets: each one stands for the set of all real numbers.)