The Regularized Inverse

Why inverting fails in the wild

An objective with two terms

The meaning of lambda

A first worked inversion

A camera with a smooth averaging matrix is inverted exactly, and the sensor readings carry small noise. What characteristically happens to the recovered scene?

In the regularized inverse $\mathbf{B} = (\mathbf{A}^T\mathbf{A} + \lambda\mathbf{I})^{-1}\mathbf{A}^T$, what happens as $\lambda$ grows very large?

A two-to-one averaging camera has $\mathbf{A} = \begin{bmatrix} 1 & 1 \end{bmatrix}$ and reports the reading $8$, so every fitting scene pair sums to $8$. The pairs $(2, 6)$ and $(5, 3)$ both fit. What is the sum of every fitting pair?