In my understanding, a matrix is all of those: 1. a transformation in a vector space, 2. a funct

linziboobeary1o8p

linziboobeary1o8p

Answered question

2022-05-12

In my understanding, a matrix is all of those:
1. a transformation in a vector space,
2. a function form some domain to some range,
3. a shorthand way of describing a system of linear equations.
By the last point, a real-valued matrix can have any conceivable real numbers as elements. Is that true or does there exist a table of numbers, which cannot be interpreted as a matrix in the linear algebra sense?

Answer & Explanation

Mackenzie Zimmerman

Mackenzie Zimmerman

Beginner2022-05-13Added 15 answers

Actually, a matrix is simply a rectangular array of numbers. It is not a linear map, although a linear map f between two finite-dimensional vector space can be reconstructed from the matrix of f with respect to two bases. It is also not a function. And, again, it is not a system of linear equations, although such a system can be condensed through a matrix.
And, in particular, yes, any rectangular table of numbers is a matrix.

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