# Questions tagged [svd]

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics.

744 questions
22 views

### Model reduction of estimated state space models - System identification

Assume that we have a dynamical model in form of this simple transfer function $$G(s) = \frac{1}{2s^2 + 5s + 4}$$ G = tf(1, [2 5 4]) We do a step response with ...
27 views

### Rank of covariance matrix

I am having a problem with rank deficiency in a covariance matrix. I have a data-set of M variables and N observations, M>N. Calculating the singular value decomposition of the data-sets covariance ...
20 views

20 views

### Understanding singular value decomposition example

I wanted to view SVD in action (using Octave) by running it on an image and then breaking it down into a set of rank 1 matrices. I'm getting stuck before that though, because I'm unable to reproduce ...
19 views

40 views

### What's the reason to use Singular Value Decomposition instead io $(A^TA)^{-1}A^T$ for pseudo inverse?

I wonder what's the reason to use this formula from Singular Value Decomposition $$A = U\Sigma V$$ $$A^{\dagger} = V\Sigma^{-1}U^T$$ Instead of $$A^{\dagger} = (A^TA)^{-1}A^T$$ Both give ...
26 views

### Singular Value Decomposition of a rank 1 matrix

I understand that when I do SVD of a rank 1 matrix constructed as $xx^T=U\Sigma U^T$, where U=$\frac{x}{\Vert{x\Vert}}$. But when I calculate $UU^T$ I do not get the identity matrix. What am I doing ...
81 views

### Finding SVD of a linear operator (in matrix form)

The linear operator $T\in \mathcal{\mathbb{R}^2}$ defined by $T(x,y)=(2y,x)$ has singular value decomposition (SVD) $$T(x,y) = 2\langle (x,y), (0,1)\rangle (1,0)+1\langle (x,y),(1,0)\rangle (0,1).$$ ...
52 views

8 views

33 views

11 views

### Using SVD to generate a transformation for calibration

Given the problem of trying to find a transformation matrix from one camera to another on a vehicle in a calibration room with the usual checkerboard floor and walls, we can capture images from both ...
I have a matrix $A$ ...