Why isn't the least squares predictor $\Phi(\Phi^\top\Phi)^{-1}\Phi^\top$ simply the identity matrix?
378
Does $\hat{\beta}=(X′X)^{−1}X′ \ Y$ simplify further?
87635
Why cannot I obtain a valid SVD of X via eigenvalue decomposition of XX' and X'X?
82148
Why is ridge regression called "ridge", why is it needed, and what happens when $\lambda$ goes to infinity?
155765
How to derive the covariance matrix of $\hat\beta$ in linear regression?
87448
Why is a sample covariance matrix singular when sample size is less than number of variables?
52246
Is it possible Fisher information matrix be indefinite?
70723
Why are nonsquare matrices not invertible?
76853
Interpretation of $\mathbf{y}^T(\mathbf{I}-\mathbf{H})\mathbf{y}$ in OLS
77204
Least squares invariant under transformation?
109471
The eigenvectors of the transpose operator
87318
Why are symmetric positive definite (SPD) matrices so important?
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
16644
Why does cancellation of dots $\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$ work?
71231
Determinant of circulant-like matrix
66714
Characteristic polynomial of companion matrix
112428
Existence of least squares solution to $Ax=b$
17394
Sign of determinant when using $det A^\top A$