Matrix indices: Difference between revisions
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[[Category:Ambiguities]] | |||
It's common to write the entries of a matrix \(A\) as \(a_{ij}\) without a comma: | It's common to write the entries of a matrix \(A\) as \(a_{ij}\) without a comma: | ||
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a_{n1}&a_{n2}&\dots&a_{nn} | a_{n1}&a_{n2}&\dots&a_{nn} | ||
\end{array}\right)\) | \end{array}\right)\) | ||
This is an exception to [[Juxtaposition means combine in the obvious way]]. | |||
But it's also common to write the entries of a vector \(\mathbf{a}\) as \(a_i\): | But it's also common to write the entries of a vector \(\mathbf{a}\) as \(a_i\): | ||
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This is perhaps most ambiguous for expressions like \(a_{2n}\) where we could be talking about the \(2n\)th entries in a vector or an entry in the 2nd row of a matrix. | This is perhaps most ambiguous for expressions like \(a_{2n}\) where we could be talking about the \(2n\)th entries in a vector or an entry in the 2nd row of a matrix. | ||
Latest revision as of 15:01, 10 July 2021
It's common to write the entries of a matrix \(A\) as \(a_{ij}\) without a comma:
\(A = \left(\begin{array}{cccc} a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{nn}\\ \vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&\dots&a_{nn} \end{array}\right)\)
This is an exception to Juxtaposition means combine in the obvious way.
But it's also common to write the entries of a vector \(\mathbf{a}\) as \(a_i\):
\(\mathbf{a}=\left(\begin{array}{c}a_1\\a_2\\\vdots\\a_n\end{array}\right)\)
\(a_{12}\) could represent either the entry 1,2 in a matrix, or the 12th entry in a vector. \(a_{112}\) could represent a whole range of things.
This is perhaps most ambiguous for expressions like \(a_{2n}\) where we could be talking about the \(2n\)th entries in a vector or an entry in the 2nd row of a matrix.
