Matrix: Transpose

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We can use the GNRNDM program with the key values 46307301801, 3741425362 and 0 to generate the matrices:

The calculator used to obtain the images below was a TI 84 Plus running the 2.55MP operating system and it was in the CLASSIC display mode. These images merely reflect generating the matrices.

To form the transpose of a matrix we we rewrite the matrix changing each row to a column. Thus, We indicate that we want to use the transpose of a matrix with the unary postfix operator ^T, meaning that we put the operator after the matrix that we want to transpose. Thus the tanspose of [A] is written as [A]^T.

One might ask why we would want to do this. For our purposes we can just observe that a matrix such as For us, the transpose is just a convenient way to write a matrix so that it takes less room to display. The images below walk us through finding the transpose on the TI-83/84 calculators.

Figure 01	To find the transpose of [A] we will need to donstruct the command [A]^T. To do this we open the matrix menu as shown in Figure 01. Then, because the desired matrix is already highlighted we can press to paste that name onto the home window.
Figure 02	Figure 02 shows that we have the name of the desired matrix on the home window.
Figure 03	We return to the matrix menu, use to move tot he MATH option and then use to highlight the ^T item as shown in Figure 03. Then press to paste that onto our command.
Figure 04	Now that the command is correctly formed, as in Figure 04, we press to have the calculator perform the command.
Figure 05	The result, or at least the first four and a bit of the fifth column, is shown in Figure 05.
Figure 06	We can use the key to slide the display over so that we can see the rest of the matrix, as shown in Figure 06. We note that the transposed matrix is exactly as we had expected from the discussion above.
Figure 07	Recall that [B] is a `5 x 3` matrix so we expect that [B]^T will be a `3 x 5` matrix. Figure 07 shows the command needed to find the transpose of [B].
Figure 08	Figure 08 shows the result of that transpose, although again we can only see part of the answer.
Figure 09	The rest of the resulting matrix is shown in Figure 09.
Figure 10	For Figure 10 we form and execute the command to find the transpose of [C].
Figure 11	For Figure 11 we form and execute the command to find the transpose of [D].
Figure 12	For Figure 12 we simply add the command to find [E] transpose. .
Figure 13	Figure 13 shows the result, again a value that showl be compared to the value of the original matrix [E].
Figure 14	Finally, in Figure 14, we see a demostration of the fairly obvious fact that the transpose of the transpose of a matrix is just the original matrix.