Placeholders

Posted byRobert SterlingPosted inTensors

We may have a story where we believe a 3×3 matrix is needed to convert a first thing to a second thing. We may choose a notation, a way of typing symbols, to build that 3×3 matrix even though we do not yet know what the numbers are.

\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{33} & a_{32} & a_{33} \end{bmatrix} = \begin{bmatrix} 3 \\ 6 \\ 9 \end{bmatrix}

At this point we don’t know any of the a’s. We just believe, or maybe even have definitively proof, that an answer exists. right now, all those a’s are just placeholders.

Oh, for this particular problem, we can make the equality true by setting a11, a22 and a33 all to a value of 3 and giving all the others a value of 0.

Leave a comment