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## Main Question or Discussion Point

Every book I've seen starts out with "to find the transpose, make B_ij = A_ji . However, they don't explain exactly why would would want to do this.

Ie. they tell you the inverse is useful because if you have Ax = b, you can find x by writing b = A^{-1} x.

The only thing I can think of to do with the transpose is visualize the row space by plotting A^T x where x is a bunch of vectors from a unit circle.

Does anyone have anything better to say about transposes?

Thanks,

Dave

Ie. they tell you the inverse is useful because if you have Ax = b, you can find x by writing b = A^{-1} x.

The only thing I can think of to do with the transpose is visualize the row space by plotting A^T x where x is a bunch of vectors from a unit circle.

Does anyone have anything better to say about transposes?

Thanks,

Dave