Recall that we know how to add two signal/vectors and scale a vector/signal.

A vector space

Depending on whether
α ∈ R
α
or C we can distinguish real
vectors spaces from complex vector spaces.

a line in

a line in

a plane in

...

Vector spaces?

A subspace of a vector space is a subset of the vectors that is itself a vector space.

Vectors lying in a line through the origin in

Fundamental idea in DSP: split the vector space of all signals into "signal space" and "noise space". Why is this reasonable?

Show that the set of all linear combinations of

If a vector space consists of all linear combinations of

The vector

The canonical

Can

Do

Is