Through learning the idea of Vector space and more kinds of spaces, how can I strengthen the abstract mathematical sense of Linear Algebra.
Let me say clearer. When I am learning Linear Algebra by the open video of 18.06, I can feel what Mr.Strang want to express and experienced some strong ideas. However, i am a person who always want to insist on getting to the bottom of the matter. During, it seems that i gradually lost the key idea of Linear Algebra and met so many difficulties which is hard to express by myself. I read Linear algebra done right

Question

Through learning the idea of Vector space and more kinds of spaces, how can I  strengthen the abstract mathematical sense of Linear Algebra.
Let me say clearer. When I am learning Linear Algebra by the open video of 18.06, I can feel what Mr.Strang want to express and experienced some strong ideas. However, i am a person who always want to insist on getting to the bottom of the matter. During, it seems that i gradually lost the key idea of Linear Algebra and met so many difficulties which is hard to express by myself. I read Linear algebra done right

anonymous · Answer

I'm not sure exactly what you're asking, but the best way to understand a mathematical discipline intuitively is to use it.  Try using the tools of linear algebra to actually accomplish a task.