09/29 - Analogy to Vector Spaces

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Analogy to Vector Spaces

Let the vector be defined as:

    • are the coefficients
    • are the basis vectors
    • A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of

Dot Product & Inner Product

Dot Product

The dot (scalar) product takes two vectors over the real numbers and returns a real-valued scalar quantity. Geometrically, it will show the projection of one vector ?set? onto another ?set?.

Mathematically the dot product of two vectors and is defined as

Inner Product

Since we will be dealing with complex numbers, we need to use the inner product instead of the dot product