Why do transformation matrices always have an extra dimension?
108545
Why does a translation matrix need extra row?
114271
Why is a matrix invertible if it can be written as the product of elementary matrices?
66539
Why is the determinant the volume of a parallelepiped in any dimensions?
44721
Dimension of Dirac $\gamma$ matrices
58595
Existence of a G-invariant matrix
127719
Is the matrix $R$ in the $QR$ decomposition unique?
1162
Why $\{\mathbf{0}\}$ has dimension zero?
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
24615
Why should transcendental functions and their arguments be dimensionless?
101185
Jacobian Matrix in dynamical systems
19499
Why is cross product only defined in 3 and 7 dimensions?
53772
What's the explicit categorical relation between a linear transformation and its matrix representation?
125816
Why is there no simpler form of a matrix than the Jordan or Frobenius normal form?
78828
Intuitive explanation for density of transformed variable?
80623
Must $S$ be a unitary matrix?
49766
Examples of results failing in higher dimensions
70245
Why is the eigenvector in PCA taken to be unit norm?