Linear Algebra

Dot Product

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Cross Product (vector product)

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The magnitude of the cross product equals the area of a parallelogram with the vectors for sides.

In particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The units of the cross-product are the product of the units of each vector. If two vectors are parallel or are anti-parallel (that is, they are linearly dependent), or if either one has zero length, then their cross product is zero.

The outer product PXQ can also represent a linear change in vector Q based on vector P. Linear transformation refers to the process of converting one vector to another vector by matrix multiplication. In three dimensions, any linear transformation can be represented by a 3x3 matrix.