The determinant of an anti-diagonal matrix has absolute value given by the product of the entries on the diagonal from the lower left corner to the upper right corner.

The physical significance of the off-diagonal components is that you're using a coordinate system not aligned with the principal directions of the object. They tell us nothing interesting about the …

Apr 16, 2025 · In this paper we extend the theory of Rubio de Francia extrapolation for matrix weights, recently introduced by Bownik and the first author, to off-diagonal extrapolation.

Off-diagonal elements in a matrix are the elements that are not on the main diagonal. The main diagonal of a matrix consists of elements where the row and column indices are the same, like …

Jul 1, 2020 · Here $U$ is the unitary matrix of eigenvectors of $M$; the eigenvalues are contained in the diagonal matrix $\Lambda$.

In the realm of linear algebra and data analysis, the term “off-diagonal element” refers to the elements of a matrix that are not located on the main diagonal.

Jul 27, 2024 · Let $\mathbf A = \sqbrk a_ {m n}$ be a matrix. The off-diagonal elements of $A$ are the elements of $\mathbf A$ which do not lie on the main diagonal of $\mathbf A$.

Dec 1, 2023 · Q: What is an off-diagonal matrix in R? A: It’s a matrix where the elements are shifted off the main diagonal, useful in various data analysis and machine learning scenarios.

As stated above, a diagonal matrix is a matrix in which all off-diagonal entries are zero. That is, the matrix D = (di,j) with n columns and n rows is diagonal if. However, the main diagonal …

People sometimes refer to "the entries above the main diagonal" of a matrix. For example, https://mathematica.stackexchange.com/questions/41362/how-to-select-all-elements-above …