Lec 4 - Subspace & Dot Product

Wednesday, January 11, 2012

9:26 AM

Recall:

Definition

Theorem: (Subspace Test)

Proof:

Properties 1 and 6 are what is being checked.

Note: Our proof shows that any set that does NOT contain the zero vector is NOT a subspace.

Eg.

Eg.

=0

Property 4 holds true.

Note:

Eg.

Dot Product

Definition

Note: The result of the dot product is a scalar, NOT a vector.

Eg

Theorem (Properties of Dot Product)

Proof:

Q.E.D.

Definition

Eg.

Definition

Theorem: (Property of Norms)

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