Linear (Vector) Space
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The axioms of a linear (vector) space, examples and counterexamples.
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Search results for “algebra”
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47 results
Basis, Dimension, and Span
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Linear dependence of vectors, basis and coordinates, dimension, subspaces, and linear span.
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Linear Operator
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A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.
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Eigenvectors and Eigenvalues
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Eigenvectors and eigenvalues, the characteristic equation, eigenspaces, and diagonalization of matrices.
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Change of Basis
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The change-of-basis matrix, recomputing a vector's coordinates and an operator's matrix, and the orthonormal case.
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Quadratic Forms
2026TheorySergey
Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.
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