During my second course in linear algebra, I encountered a frequent need to convert linear maps into matrices. This task became particularly challenging when working with complex maps and bases, ...
Consider $T = (x_1,..,x_5) \to (x_4, x_5)$. We have $\operatorname{null} T = \{(x_1,x_2,x_3,0,0) | x_1,x_2,x_3 \in \mathbb{F}\}$, and $\operatorname{range} T ...
Linear maps are abstractly defined things. We’d like to make them concrete. We do this by making the following observation: once you know what a linear transformation does on a basis, you know what it ...
1 Department of Mathematical Sciences, Mathematical Finance and Econometrics, Catholic University of the Sacred Heart, Milan, Italy 2 Department of Economics, University of Bamberg, Bamberg, Germany ...
But an arbitrary function between two vector spaces doesn’t necessarily give you any information about their relationship as vector spaces. To get such information, we need to restrict to functions ...
CBSE Class 12 Maths Mind Map Linear Programming: The Central Board of Secondary Education (CBSE) is a popular school board in India and conducts the year-end board exams for lakhs of students. It’s ...
1 Department of Computer Science, Colorado State University, Fort Collins, CO, United States 2 Department of Mathematics, Colorado State University, Fort Collins, CO, United States In the ...
Linear algebra is essential for understanding core data science concepts like machine learning, neural networks, and data transformations. Different books cater to various needs. Some focus on ...
How these long-term oscillations emerge, and why they have variable periods and only occur in a subset of cell lineages remain unclear. At a fundamental level, oscillations require negative feedback, ...
Some results have been hidden because they may be inaccessible to you
Show inaccessible results
Feedback