Inverse Matrices
2026TheorySergey
Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.
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Works
290 results
Properties of Determinants
2026TheorySergey
The basic properties of determinants with brief proofs, and their use in simplifying computations.
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Determinant via Permutations
2026TheorySergey
The direct definition of a determinant via permutations: inversions, parity, and a sum of n! terms.
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Determinant
2026TheorySergey
The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
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Properties of Matrix Operations
2026TheorySergey
The basic properties of addition, scalar multiplication, transposition, and multiplication of matrices, with justifications.
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Basic Operations on Matrices
2026TheorySergey
Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.
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Charge Collection After Heavy-Ion Strikes: A Material Parameter Sweep in a 2001 TCAD Solver
2026NotesAlexey Legoshin
A pilot study mapping ion-induced charge collection against bandgap and carrier mobility, and what it revealed about the cost of getting the time integration wrong
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ISE TCAD 7.0 on Apple Silicon: Running a 2001 Semiconductor Package on a MacBook Air M1
2026NotesAlexey Legoshin
How to bring up a twenty-year-old Unix TCAD package under emulation on an ARM Mac, drive it from Jupyter, and parse its data formats in Python
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Integrals with Trigonometric Functions
2026ReferenceSergey
Reference table of indefinite integrals of sine, cosine, tangent and their powers and products.
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Integrals of Trigonometric Functions and Monomials
2026ReferenceSergey
Reference table of indefinite integrals of products of powers of x with sine and cosine.
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