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Works

290 results

Quadratic Forms

Jul 24, 2026TheorySergey

Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.
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160

Change of Basis

Jul 24, 2026TheorySergey

The change-of-basis matrix, recomputing a vector's coordinates and an operator's matrix, and the orthonormal case.
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220

Linear Operator

Jul 24, 2026TheorySergey

A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.
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150

Systems of Linear Equations

Jul 24, 2026TheorySergey

Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.
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210

Matrix Rank

Jul 24, 2026TheorySergey

Minors and the rank of a matrix, invariance of rank under elementary transformations, and a practical method for computing it.
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190

Inverse Matrices

Jul 24, 2026TheorySergey

Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.
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120

Determinant

Jul 24, 2026TheorySergey

The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
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190

Basic Operations on Matrices

Jul 24, 2026TheorySergey

Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.
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150

Matrices

Jul 24, 2026TheorySergey

A matrix, its notation, and the main types: row, column, echelon, square, diagonal, identity, symmetric - defined and shown with worked examples.
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570