techtree / Linear algebra

Matrices

A matrix is a grid of numbers; a stack of vectors.

35 seconds

\underbrace{\begin{bmatrix} 2 & -1 & 4 \\ 0 & 3 & 7 \end{bmatrix}}_{2 \times 3}

Transcript

A matrix is a grid of numbers.

This one has two rows, and three columns. We call it two by three.

Read it down, and each column is a vector. One, two, three vectors, side by side.

Read it across, and each row is a list of numbers too.

Every entry has an address: row first, then column. Row two, column three holds a seven.

Matrices come in any shape. Tall, wide, or square.

A matrix with just one column is simply a vector.

A grid of numbers, or vectors side by side. Same thing.

Needs

Matrix times vector video
Each output entry is a dot product of one row with the vector.
Transpose video
Flip a matrix so rows become columns.