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Suppose A1 and A2 are two full rank matrices of similar size. What could be the parameter which say that one of matrix have more independent vectors compared to another matrix?

In other words, column vectors of one matrix are more orthogonal among themselves compared to another matrix.

Could Determinant be the right measure to differentiate two matrices?

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Assuming the column vectors are normalized (and A1 and A2 have the same dimensions), the (absolute value of) determinant is in fact a measure of the level "independency" as the former is equivalent to the volume of the parallelepiped spanned by the column vectors in high dimensions; you can visualize in 2D/3D that the more orthogonal the unit vectors are, the bigger volume they create.

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