techtree / Linear algebra

Transpose

Flip a matrix so rows become columns.

33 seconds

[2−14037]T=[20−1347]\begin{bmatrix} 2 & -1 & 4 \\ 0 & 3 & 7 \end{bmatrix}^{\mathsf{T}} = \begin{bmatrix} 2 & 0 \\ -1 & 3 \\ 4 & 7 \end{bmatrix}
Transcript

Here is a matrix with two rows and three columns.

To transpose it, turn every row into a column. The first row becomes the first column. The second row becomes the second column.

Two by three becomes three by two.

Another way to see it: flip the grid over its diagonal. The entry in row one, column three lands in row three, column one.

Transpose it again, and you are back where you started.

It is written with a small T. Rows become columns, and columns become rows.

Needs

  • Matrices video
    A matrix is a grid of numbers; a stack of vectors.
Everything this builds on (2 topics, in order)
  1. Vectors
  2. Matrices

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