# What does it mean for a matrix to have rank 0 ( zero) ?

## Main Question or Discussion Point

What does it mean for a matrix to have rank 0 ( zero) ?

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quasar987
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The rank of a matrix is the dimension of the image of the linear map it represent. Since the only vector space of dimension 0 is the vector space denoted 0 consisting of only one elements (namely, 0), to say that a matrix is of rank 0 is to say that the image of the linear map it represents is the vector space 0.

You can convince yourself that, in turn, this implies that the matrix is the matrix 0 (the matrix having 0 in all its entries...)

Thanks quasar987.

So a matrix with atleast one non-zero element will have atleast rank 1 ?

matt grime