BIZNIQUE / LINEAR ALGEBRA / 03
Transpose a matrix
Transpose a matrix
Watch rows become columns without changing the underlying entries.
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THE IDEA
Read the example.
Read the example.
Transposition changes an m-by-n matrix into an n-by-m matrix. The value at row i, column j moves to row j, column i. It is a change in orientation, not an inverse operation.
(Aᵀ)ᵢⱼ = Aⱼᵢ
Use it well
Use it well
Transposition reverses product order: (AB)ᵀ = BᵀAᵀ. It does not normally leave AB in the same order.
TRY IT YOURSELF
A quick check.
A quick check.
Transpose [[1, 2, 3], [4, 5, 6]].
Check your reasoning
Check your reasoning
The result is [[1, 4], [2, 5], [3, 6]], with three rows and two columns.
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