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What? They're a convenient device for writing down a linear map between finite-dimensional vector spaces. Nothing more, nothing less. Your explanation is bound

• raverbashing 6y ago
  Yes they're mundane, but the "linear map between different vector spaces" case is pretty much the only thing they can do. Think of it as type casting in programming languages, you only do it when you need, but the real work is done processing elements of the same type. If that wasn't the case, then non-square matrices would have all the "cool" properties of the square ones. Yes I might be picking at straws here, and I agree it might confuse people even more, but this weirdness of matrices hasn't escaped me since I've learned about it. And then when you get to vectors it all makes sense. Hum...
  • gspr 6y ago
    > Yes they're mundane, but the "linear map between different vector spaces" case is pretty much the only thing they can do. Of course it's all they "can do". They're merely a way of writing down linear maps for a given choice of bases.
    • raverbashing 6y ago
      Yes. Then they're a "different" object than a square matrix or a vector. My point is, the sub-algebra of all square matrices supports more operations than mixing matrices of different sizes.