Aug 19, 2020 · Defines a left-aligned text control. The control is a simple rectangle displaying the given text left-aligned in the rectangle. The text is formatted before it is displayed.

Static Text Statements: LTEXT, CTEXT and RTEXT. Each of these statements creates a static text control. The control is a simple rectangle displaying the given text, which is either aligned to one edge or centered in the rectangle. The text is formatted before it is displayed.

Dec 11, 2024 · If I have a matrix $X\in \mathbb{R}^{n\times p}$, then I can write the covariance as $$\text{Cov}(X) = \mathbb{E}[(X-\mu_X)(X-\mu_X)^T]$$ Now, assuming the data is centered, this becomes $\text{Cov...

Mar 17, 2017 · Consider a simple regression without a constant term, and where the single regressor is centered on its sample mean. Then X′X X ′ X is (n n times) its sample variance, and (X′X)−1 (X ′ X) − 1 its recirpocal.

Jan 31, 2018 · Did you know that for any matrix $latex X \in \mathbb {R}^ {m \times n}$, the matrix $latex X^TX$ is positive semidefinite (PSD)? The proof is literally one-line: for any vector $latex z \in \mathbb {R}^n$, $latex z^T (X^T X)z = (Xz)^T (Xz) = \|Xz\|_2^2 \geq 0.$ Note that this applies for real matrices of any size. It also…

Jan 21, 2020 · Let x = ⎡⎣⎢x1... xn ⎤⎦⎥ x = [x 1... x n] and therefore xT =[x1... xn] x T = [x 1... x n]. If you evaluate x ⋅xT x ⋅ x T you multiply the rows of x (just one entry) with the columns of xT x T with also just one entry. This gives you the matrix. This is also called a dyadic product.

Jun 4, 2018 · Prove, for real $X$, that $\text{rank}(X^TX)=\text{rank}(X)$. Could anyone please help me with this problem? I've tried to use full-rank factorization and rank-related theorems mentioned in my boo...

In least squares estimation where Y = βX Y = β X, how can we find the correlation matrix of X X in terms of XTX X T X? It seems that XTX X T X is very close in structure to the correlation matrix, but don't know how to get the last step. Are you referring to the variance-covariance matrix of the β^ β ^ estimators?

λtext turns text files into higher-order functions, featuring a Hindley-Milner / prenex polymorphic type system. See the github.io page. This should install in one pass; all the non-stackage dependencies are included in stack.yaml. You can build with nix with the following command: [--left LEFT] [--right RIGHT]

Our algorithm, called eXploit-Then-eXplore (XTX), begins each episode using an exploitation policy that imitates a set of promising trajectories from the past, and then switches over to an...