Linear Algebra | JRF EXPRESS | CSIR NET June 2026 | Lec-04 | IFAS

Linear Algebra | JRF EXPRESS | CSIR NET June 2026 | Lec‑04 | IFAS explained with clear concepts and exam‑focused approach. Covers Linear Algebra PYQs with characteristic polynomial tricks, orthogonal complement dimension shortcuts, and linear map isomorphism – all with problem‑solving strategies for CSIR NET aspirants. 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/mathe... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:00:00] – Introduction to Linear Algebra [00:02:50] – Question 1: Inner Product Space [00:11:56] – Question 2: Idempotent Matrix [00:20:06] – Question 3: Span Dimension (Trig) [00:30:31] – Question 4: Matrix Identities [00:40:08] – Trick: AB & BA Eigenvalues [00:42:08] – Question 5: Jordan Canonical Form [00:46:56] – Question 6: Real Eigenvalues (3×3) [00:55:19] – Homework: Countable Sets [00:57:01] – Complete Session (Linear Algebra) ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: • Characteristic Polynomial via Trace & Determinant • Minimal vs. Characteristic Polynomial PYQ • Orthogonal Complement Dimension Shortcuts • First Isomorphism Theorem for Linear Maps • Subspace Union Condition & PYQ Problems • Linear Algebra JRF EXPRESS Problem‑Solving ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty focuses on solving Linear Algebra PYQs for CSIR NET June 2026 under JRF EXPRESS. Key tricks include deriving the characteristic polynomial of a 3×3 matrix from its trace, trace of square, and determinant, the dimension relation dim(W) + dim(W per) = dim(V), and applying the first isomorphism theorem to show a map onto ℝ³. Union of subspaces and invertibility‑similarity problems are also covered, making linear algebra concepts exam‑ready. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 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 📘 Free Counselling: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 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   #linearalgebra #jrfexpress #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetjune2026 #csirnetlecture #ifasmathematics