Testwiki:Reference desk/Archives/Mathematics/2022 September 15

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September 15

matrix equivalence

Hi,

Why can we say that the two following matrices :

$\left(\begin{array}{c}{\overrightarrow{y}}_1\\ ⋮\\ \overrightarrow{u}⋮\\ \overrightarrow{n}x\end{array}\right)=\left(\begin{array}{cccc}\overrightarrow{1}& x_{\overrightarrow{1},1}& \ddots & x_{800,p}\\ \ddots & ⋮& ⋮& \cdots \\ 1& x_{n,1}& \overrightarrow{5}\end{array}\right)::$

are equivalent matrices? 87.88.174.86 (talk) 02:28, 15 September 2022 (UTC)

Where did you find this symbolic matrix equality? It uses strange notations that do not make sense to me. Whatever they may mean, given two matrices $A$ and $B$ of the same shape, one may assume they are equal (as an assumption in a proof), one may require them to be equal (as something that is given in a subsequent proof), or one may (hope to) prove they are equal. $A=B$ then means the same as $A_{i,j}=B_{i,j}$ for all corresponding matrix entries. I would need to see the context to understand why the author used the term "equivalent" instead of the simpler "equal".  --Lambiam 03:19, 15 September 2022 (UTC)