I'm having difficulty understanding the Transpose
function. I know what the transpose of a matrix is, not a problem, and I see that applying the Transpose
function to a 3×3 matrix does what is expected.
What I am having difficulty with is the definition, which says:
Transpose[list]
, "transpose the top two levels of list"
Consider:
A = {{a, b}, {c, d}}
Transpose[A]
What does it mean when the definition says "transpose the top two levels of the list?"
I've read about levels in lists, experimented with TreeForm
, but something like this is giving me a lot of trouble.
A = {{{a, b}, {c, d}}, {{e, f}, {g, h}}, {{i, j}, {k, l}}}
Transpose[A, {3, 1, 2}]
Can someone help me (gently) understand the definition:
Transpose[list,{n1,n2,...}]
, "put the $k^{th}$ level in list at level $n_k$" ?