Vectors

For now, you can just think of vectors as tuples written a different way. Instead of the tuple \(\left \langle a,b,c \right \rangle\), one could write the column vector

\[\begin{pmatrix} a\\b\\c\\ \end{pmatrix}\]

or the row vector

\[\begin{pmatrix} a & b & c\\ \end{pmatrix}\]

Row vectors may also be written with commas between their elements, e.g. \((a, b, c)\), at which point they really look just like tuples but with parentheses instead of pointy brackets.

Rewrite each one of the following as instructed

  • \(\left \langle 10, 7, 5, -2.3 \right \rangle\) as a column vector
  • \(\begin{pmatrix} 1 & 0 & 0 & 1 & 0 \end{pmatrix}\) as a tuple
  • \(\left \langle \mathrm{True}, \mathrm{False} \right \rangle\) as a row vector
  • \(\left \langle 0 \right \rangle\) as a column vector

Once I have more time to expand this unit, you’ll learn a bit more about the intuition behind vectors.