What is the Dimension of a Matrix in R^(2x3)?

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SUMMARY

A matrix in R^(2x3) has a dimension of six, which corresponds to the total number of independent entries within the matrix. Specifically, this dimension refers to the vector space formed by all possible 2x3 matrices, indicating that there are six degrees of freedom in selecting the entries. The discussion clarifies that while the number of columns is relevant, the dimension of the matrix itself is defined by the total count of independent elements.

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Niles
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Homework Statement


If we have a matrix in R^(2x3), what dimension does this matrix have?

My book doesn't answer this question - it only tells me what the dimensions are of the different spaces, not of the matrix as a whole.

The Attempt at a Solution


I would think the dimension is the number of columns, but it's just a guess. I hope you guys can clarify this for me.
 
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There are six independent numbers in a 2x3 matrix. So the dimension of the vector space of 2x3 matrices is six. That's the only sense I can think of to talk about the 'dimension' of a matrix.
 
I see.. thanks!
 

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