# Tag Info

1 vote

### Does $X, X^t$ have same operator norm.

\begin{align} \left\|X\right\| &= \max_{\left\|h\right\|=1} \left\|Xh\right\|\\ &= \max_{\left\|h\right\|=1} \left\|\overline X^T h\right\|\\ &= \max_{\left\|\overline h\right\|=1} \left\|\...
1 vote
Accepted

### When does a real symmetric matrix have $LDL^{T}$ decomposition? And when is the $LDL^{T}$ decomposition unique?

Let us answer the questions one by one: Point1: The factorization $LDU$ relies on the factorization $LU$ and then we use $D$ to make $U$ as an upper triangular matrix with $1$'s in the main diagonal. ...
1 vote
Accepted

### To compute Hermite Normal Form H and U

To undestand how the process works, it is best illustrated with a non-squared matrix. As square matrices are easier to work with, it doesn't show the full extend of the process. Process: The intuitive ...
1 vote

### Gram matrix of QR decomposition

The projection $\hat x$ of $x$ onto the image of $A$ is $$\hat x = A(A^T A)^{-1} A^T x. \tag{1}$$ so $y = x - 2 A(A^T A)^{-1} A^T x$. This is a well known formula in the topic "linear ...

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