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The linear filtering of color images using hypercomplex convolution and Fourier transforms provides a holistic treatment of color by representing pixels as 3-space vector quantities within the quaternion algebra. But, this technique is limited to images with at most three channels of information, e.g., RGB images. Linear filtering of color images by representing color pixels as multi-vectors embedded in a geometric algebra is presented. This multi-vector representation has similar convolution and Fourier transforms as the quaternion based filters, but provides an avenue for multi-spectral images composed of more than three channels.