Search results for “SAGE”
Categories
48 results
Determinant
2026TheorySergey
The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
0
190
Properties of Determinants
2026TheorySergey
The basic properties of determinants with brief proofs, and their use in simplifying computations.
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260
Matrix Rank
2026TheorySergey
Minors and the rank of a matrix, invariance of rank under elementary transformations, and a practical method for computing it.
0
190
Linear Operator
2026TheorySergey
A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.
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150
Eigenvectors and Eigenvalues
2026TheorySergey
Eigenvectors and eigenvalues, the characteristic equation, eigenspaces, and diagonalization of matrices.
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170
The Steinberg Representation
2026TheorySean Cotner
An introduction to the Steinberg representation of a finite group of Lie type — its alternating-sum construction from parabolic inductions, worked out explicitly for SL_2.
0
270
Machine Learning 2. Lecture 3. Vector Representations of Texts and Graphs
2026LectureКонстантин Вячеславович Воронцов
Vector representations (embeddings) of texts and graphs: the distributional semantics hypothesis, syntagmatic and paradigmatic similarity of words, the CBOW and Skip-gram models of the word2vec program, hierarchical SoftMax on a Huffman tree, negative sampling (SGNS) and the connection of word2vec with the matrix factorisation of the PMI matrix, semantic analogies of words, the FastText model on character n-grams; texts as graphs; multidimensional scaling and the stress criterion, stochastic neighbour embedding SNE, perplexity, t-SNE; matrix factorisations of graphs, the random-walk models DeepWalk and node2vec; graph embedding methods as autoencoders, the generalised GraphEDM model, graph neural networks and message passing.
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250