DIAGONALIZATION -| | Lec-17 | CSIR NET MATHEMATICS | IFAS

Diagonalization and Jordan Canonical Form in Linear Algebra explained with clear concepts and exam-focused approach. Learn minimal polynomial, nilpotent matrix, eigenspace, similar matrices, block diagonal matrices and idempotent matrix for CSIR NET, GATE and SET. 🧭 Get Personalized Preparation Guidance: https://ifasonline.com/csir-net/mathe... 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/mathe... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00] Introduction [02:44] Session Start [04:08] Q1: Jordan Canonical Form [05:00] Characteristic and Minimal Polynomial [06:01] Nilpotent Index 2 [06:32] Q1 Answer: A, B, C [08:25] Q2: Diagonalizable over C [10:08] Option A Analysis [12:21] Option B: Block Matrix [13:11] Option C: Block Diagonal [14:34] Option D: Involutory Operator [15:21] Diagonalizability over Any Field [16:28] Q3: Similar Matrices over Q [18:27] Jordan Form and Geometric Multiplicity [20:10] Q3 Answer: A, C, D [20:40] Q4: Possible JCF for T on R4 [23:11] Q4 Answer: A, B [23:17] Q5: 6x6 Matrix over R [26:32] Q5 Answer: B, C [28:08] Q6: Diagonalizable Conditions [31:47] Option D: n Independent Eigenvectors [33:46] Q7: 4x4 Matrix, Null Space Dimensions [36:45] AM = GM Implies Diagonalizable [37:40] Q7 Answer: A, B, D [37:54] Q8: A² = A, Eigenvalues 0 and 1 [40:05] Q8 Answer: A, C, D [42:54] Q9: 4x4 Complex Matrix, Rank 2 [45:04] Minimal Polynomial Analysis [46:50] A² = A Contradiction [47:09] Q9 Answer: A, C, D [47:16] End Of Lecture ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: Diagonalization and Jordan Canonical Form in Linear Algebra explained with clear concepts and exam-focused approach. Learn minimal polynomial, nilpotent matrix, eigenspace, similar matrices, block diagonal matrices and idempotent matrix for CSIR NET, GATE and SET. ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on Diagonalization and Jordan Canonical Form for CSIR NET, GATE and SET. Covers Jordan canonical form from minimal polynomial, nilpotent index, diagonalizability over C and any field, similar matrices over Q, possible JCF for given characteristic and minimal polynomial, geometric multiplicity, algebraic multiplicity, null space dimensions, idempotent matrix properties, rank-trace relation, and A²=A analysis. Learn shortcuts, counterexamples and exam-focused problem-solving. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics ✅ TIFR Mathematics ✅ PhD Entrance Exams ━━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for CSIR NET & GATE Mathematics? (Our Results Speak): ✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....) ✅ CSIR NET June 2025: 4200+ Selections (AIR 1, 2, 6, 10...) ✅ CSIR NET Dec 2024: 4000+ Selections (AIR 5, 6, 7, 8, 9...) ✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...) ✅ CSIR NET Dec 2023: 1200+ Selections (AIR 2, 4, 5...) 📄 View IFAS Result Sheet: 👉 https://drive.google.com/file/d/1THh6... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥CSIR NET Mathematical Science Live & Recorded Course: https://ifasonline.com/csir-net/mathe... 🎯 GATE Mathematics Recorded Course: https://ifasonline.com/gate/mathemati... 📘CSIR NET Mathematical Science Books: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 Download IFAS App: Android: https://play.google.com/store/apps/de... IOS: https://apps.apple.com/us/app/ifas/id... ━━━━━━━━━━━━━━━━━━━━━━━━━ Stay Updated Via Other Social Media: ✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu... ✔Instagram:   / csir_net_mathematical_science   #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetdec2026 #csirnetlecture #ifasmathematics