30 Projection and residual
\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]
Reading questions
What does it mean to βscaleβ a vector? What property does scaling change about the vector and what property does it leave alone?
question id: 30-reading=vector-scaling
What kind of mathematical object is produced by a linear combination of vectors?
question id: 30-reading-LC-kind-of-object
Vectors are one-dimensional objects analogous to an arrow. Those one-dimensional objects are always embedded in a space that typically has more than one dimension, just as an arrow is embedded in two-dimensional space (e.g. a piece of paper) or a three-dimensional space as in an archery range.
Explain how a vector can be embedded at the same time in a space and a sub-space.
question id: 30-reading-subspace
Explain how a vector can be made to represent a function.
question id: 30-reading-vector-function
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