Quadratic Forms See Only the Symmetric Part
An interactive live film: W splits into a symmetric and a skew-symmetric part; the skew part turns x at a right angle, so it never changes the surface xᵀWx, and exactly one symmetric matrix gives each quadratic form.
Narration
The surface is the quadratic form x transpose W x, and the matrix W is on the right. This W is not symmetric: its corners off the diagonal are two and zero.
Every square matrix splits into two parts: a symmetric part, W plus W transpose over two, and a skew-symmetric part, W minus W transpose over two.
The rest of the narration is in the book's Companion.
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