ELEC505: Linear System Theory

Comprehensive lecture notes, study guides, cheatsheets, and compiled PDF resources for ELEC505 LINEAR SYSTEM THEORY at Koç University (Spring 2026).

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📚 Course Details

• Course: ELEC505 LINEAR SYSTEM THEORY
• Institution: Koç University
• Term: Spring 2026

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📂 Repository Structure

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├── README.md
└── lectures/
    ├── study_outputs/
    │   ├── lecture_notes/             # Markdown notes (Lectures 02 to 23)
    │   ├── pdf/                       # Compiled PDF notes (individual & combined)
    │   │   ├── lecture_notes/         # PDF version of each lecture note
    │   │   ├── combined/              # Full course combined PDF notes
    │   │   └── review/                # PDF revision guides & cheatsheets
    │   └── review/                    # Last day revision & study guides
    ├── final_cheatsheet.md            # Quick-reference cheatsheet
    ├── master_notes.md                # Master summary of course concepts
    └── master_proof_notes_cheatsheet.md  # Proof & theory summary

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💡 Key Topics Covered

1. Vector Spaces & Subspaces: Span, linear independence, basis, dimension, hyperplanes, half-spaces.
2. Inner Product Spaces: Euclidean norm, Cauchy-Schwarz inequality, orthogonality, projections.
3. Fundamental Matrix Subspaces: Column space, row space, null space, left null space, rank-nullity theorem.
4. Eigendecomposition & Spectral Theory: Characteristic polynomial, eigenvalues/eigenvectors, Hermitian, unitary, and normal matrices.
5. Quadratic Forms & Factorizations: Sylvester's Law of Inertia, level sets, Cholesky, QR, Block LDU, and Schur complements.
6. Vector & Matrix Norms: $p$-norms, sparsity, Frobenius norm, induced matrix norms.
7. Singular Value Decomposition (SVD): Fundamental theorem of linear algebra, low-rank matrix approximation, Schatten/nuclear norms.