We have decided to move away from Wix and migrate to wordpress. This offers many advantages to us.
Notably we now have math support, x^2.
#invariants
The dot product of a vector with itself is always non-negative, \mathbf{v} \cdot \mathbf{v} \geq 0
The determinant of an orthogonal matrix is always 1, \det(\mathbf{O}) = 1, \text{where } \mathbf{O} \mathbf{O}^T = \mathbf{I}
The trace is invariant under cyclical permutations, \text{Tr}(\mathbf{A} \mathbf{B} \mathbf{C}) = \text{Tr}(\mathbf{C} \mathbf{A} \mathbf{B})
The trace of the matrix is invariant under changes of basis, \lambda_1 + \lambda_2 + \dots + \lambda_n = \text{Tr}(\mathbf{A})
The sum of principle minors is invariant, \text{det} \begin{pmatrix} a_{1,1} & & & \\ a_{2,1} & a_{2,2} & & \\ \vdots & & \ddots & \\ a_{n,1} & a_{n,2} & \dots & a_{n,n} \end{pmatrix} = \sum_{i=1}^n (-1)^{i+j} a_{i,j} \text{det} \begin{pmatrix} a_{1,1} & a_{1,2} & \dots & a_{1,i-1} & a_{1,i+1} & \dots & a_{1,n} \\ a_{2,1} & a_{2,2} & \dots & a_{2,i-1} & a_{2,i+1} & \dots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{i-1,1} & a_{i-1,2} & \dots & a_{i-1,i-1} & a_{i-1,i+1} & \dots & a_{i-1,n} \\ a_{i+1,1} & a_{i+1,2} & \dots & a_{i+1,i-1} & a_{i+1,i+1} & \dots & a_{i+1,n} \\ \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{n,1} & a_{n,2} & \dots & a_{n,i-1} & a_{n,i+1} & \dots & a_{n,n} \end{pmatrix}
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