0
$\begingroup$

Say, for example I have a 5 x 5 matrix, but every row and every column is filled with a zero. Is it still a 5x5 matrix or is it a 1 x 1 matrix with a zero?

|cite|improve this question
$\endgroup$
  • 1
    $\begingroup$ I would just call it a zero matrix with dimensions as needed to suit your needs. $\endgroup$ – clocktower Apr 14 '16 at 0:35
  • 1
    $\begingroup$ It is still a $5$ by $5$ matrix. You can think of it as a linear transformation from $\mathbb{R}^5$ to itself. $\endgroup$ – fred Apr 14 '16 at 0:36
  • 2
    $\begingroup$ Yes, why would the values of the entries change the size? $\endgroup$ – user296602 Apr 14 '16 at 0:36
3
$\begingroup$

It is still a $5 \times 5$ matrix. A matrix is essentially made up of three things:

1) A height (number of rows) $n$

2) A width (number of columns) $m$

3) A collection of entries (from some field) to fill up the $n \times m$ spaces.

|cite|improve this answer
$\endgroup$
4
$\begingroup$

Yes it doesn't matter if it is filled with zeros or not, if it has five rows and five columns all zero it is still a $5\times 5$ matrix

|cite|improve this answer
$\endgroup$
1
$\begingroup$

If I write $$ 0 = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ \end{pmatrix} $$ it means that the zero matrix, here simply written as $0$. is the $5\times 5$ matrix with all elements being zero $0 \in \mathbb{F}$. So it is clear one works in $\mathbb{F}^{5\times 5}$ for some field $\mathbb{F}$.

|cite|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.