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Trace (linear algebra)
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Related lectures (29)
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Linear Algebra in Dirac Notation
Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.
Convex Optimization: Notation and Matrix Norms
Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.
Spectral Analysis: Hyperbolic Surfaces
Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.
Networked Control Systems: Challenges and Opportunities
Explores challenges and opportunities in networked control systems, covering LTI systems, delays, packet drops, and consensus.
PCA: Principal Components Analysis
Covers the concept of Principal Components Analysis, focusing on representing data optimally in a basis.
Properties of the Density Matrix
Explores the properties of the density matrix, separable states, and time evolution in isolated and non-isolated systems.
Linear Operators: Traces and Boundedness
Covers the concept of linear operators, focusing on traces and boundedness.
Non-Diagonalizable Case: Two Eigenvalues (Example)
Showcases a non-diagonalizable matrix example and explores eigenvalues and eigenvectors.
Lyapunov Stability Theory: Energy Functions and Stability Analysis
Covers Lyapunov stability theory, energy functions, positive-definite matrices, and system stability analysis through examples and theorems.
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