Matrices

Define the rows, columns and units
A numerical matrix is useful only when each position has a meaning. State row order and column order beside it. For example, a sales matrix can have one row per outlet and one column per product; its entries are quantities sold.
Match quantities to prices
If S is an outlet-by-product quantity matrix, a price column P must list prices in the same product order. Then SP gives revenue in dollars for each outlet. A column of ones adds each row: \(\begin{pmatrix}a&b\end{pmatrix}\begin{pmatrix}1\\ 1\end{pmatrix}=\begin{pmatrix}a+b\end{pmatrix}\).
For two suppliers, put one price column per supplier. The resulting product has one row per order and one column per supplier. Check what each output entry means before making a comparison.
If a supplied matrix describes a one-step redistribution, explain which column is the starting category and which row is the destination. Multiply once and interpret the resulting numbers; do not assume a long-run model.

A numerical matrix is useful only when each position has a meaning. State row order and column order beside it. For example, a sales matrix can have one row per outlet and one column per product; its entries are quantities sold.

If S is an outlet-by-product quantity matrix, a price column P must list prices in the same product order. Then SP gives revenue in dollars for each outlet. A column of ones adds each row: \(\begin{pmatrix}a&b\end{pmatrix}\begin{pmatrix}1\\ 1\end{pmatrix}=\begin{pmatrix}a+b\end{pmatrix}\).

For two suppliers, put one price column per supplier. The resulting product has one row per order and one column per supplier. Check what each output entry means before making a comparison.

If a supplied matrix describes a one-step redistribution, explain which column is the starting category and which row is the destination. Multiply once and interpret the resulting numbers; do not assume a long-run model.

Matrices as numerical models

Matrices as numerical models