30 Projection and residual
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Reading questions
What does it mean to “scale” a vector? What property does scaling change about the vector and what property does it leave alone?
What kind of mathematical object is produced by a linear combination of vectors?
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.
Explain how a vector can be made to represent a function.
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