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

= September 15 =

matrix equivalence
Hi,

Why can we say that the two following matrices :



\begin{pmatrix} \overrightarrow y_1  \\ \vdots\\ \overrightarrow u \vdots\\ \overrightarrow nx \end{pmatrix}

= \begin{pmatrix} \overrightarrow 1 & x_{\overrightarrow1,1} & \ddots & x_{800,p} \\ \ddots & \vdots & \vdots & \cdots\\ 1 & x_{n,1} & \overrightarrow 5

\end{pmatrix}

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)