#Linear Algebra

When the linear algebra final exam is ONE question… but it’s a 10x10 matrix and you have to show every Gauss-Jordan step 😭 No calculator. 6 hours. 100 marks. Pain. If you’ve ever taken a college math exam, you know the feeling. 👉 Share this with a friend who hates matrices 👉 Save this for finals week 👉 Follow for daily math memes & STEM humor

Linear algebra didn’t click for me until I saw it explained visually and intuitively. These 4 videos changed how I think about ML. Save this if you’re learning seriously. If you’re starting out, I’ve also linked a free AI roadmap in my bio that might help. Links : 3Blue1Brown https://youtu.be/PFDu9oVAE-g?si=Sm8JRGwwql2Scg4s Steve brunton: https://youtu.be/ZSGrJBS_qtc?si=0JUA0InRMBZQHBju Visual Kernal: https://youtu.be/vSczTbgc8Rc?si=ntXNXwen5O_bw4o9 MIT lecture series: https://youtu.be/TX_vooSnhm8?si=oNffsnBWpRLq-lo4 Note: These are links to the specific videos, but you can explore the full playlist as well.

Matrix diagonalization #familyguy #computerscience #linearalgebra

this is gaussian elimination. like idk it just easily makes sense by graphing it. i’d rather see the visualization before the computations. #math #linearalgebra

Have you ever felt that Linear Algebra floats a bit too far from intuition, almost abstract for the sake of it?  Let’s bring it back down to earth: geometry, color, and one clear guiding idea.  The First Isomorphism Theorem isn’t an abstract trick — it’s a story you can actually see. 📐✨ Any linear map f:V→W can be taken apart into three essential moves. Here we visualize them with a color code that isn’t decorative, but logical. 1️⃣ Projection (π\piπ) We start from the original space V (🔵). We identify vectors that differ by an element of the kernel and build the quotient space V/ker⁡(f) Geometrically, arrows stop mattering: what used to be different directions collapses into points (equivalence classes). 2️⃣ Isomorphism (f~) This is the heart of the story, the bridge (🟢). This is where the “real” transformation happens. The classes of the quotient are sent directly to the image of fff. No information is lost: since the determinant is ≠0\neq 0=0, the shape may deform, but the structure — the volume — is preserved. 3️⃣ Inclusion (iii) Finally, we place that result inside the target space W (🔴). What were points in the image now germinate again as vectors living in the whole codomain. 🌟 The magic of commutativity The yellow vector v says it all without words: going the long way around the bottom is exactly the same as applying f directly across the top. f=i∘f~∘π The theorem doesn’t say “something complicated.” It says that every linear map can be understood as collapsing, deforming, and embedding. Mathematics isn’t only calculated — it’s also seen. Does this color code help you follow the flow of the transformation? I’d love to read your thoughts 👇 MerlinoMath #maths #math #physics #linearalgebra #merlinomath

✨️Code Link in bio.✨ Solve Linear Equations Easily with Cramer’s Rule! ✨ This method is a cornerstone of Linear Algebra, giving a clear way to solve systems of linear equations using determinants. ✨ If you’re a student of algebra, matrices, IIT-JEE, university math, Ap levels, or just curious about how to solve equations step by step, this video is for you! 📐 Learning math by understanding methods like Cramer’s Rule, not just memorizing tricks, gives you clarity, confidence, and real problem-solving power. 🚀

Rank(A)=n ↔️ det(A)!=0 ↔️ columns form basis ↔️ 0 not an eigenvalue ↔️ no free variables ↔️ A invertible ↔️ Ax=b has unique solution #math #mathmemes #stem #mathematics #mathematician

Eigenvalues and eigenvectors are fundamental ideas in linear algebra that describe how a transformation acts on space. When a matrix transforms a vector, most vectors change both direction and magnitude, but eigenvectors are special because they only get stretched or compressed, not rotated. The amount of stretching is given by the eigenvalue. In simple terms, if you apply a transformation and a vector stays pointing in the same direction, just scaled, then that vector is an eigenvector and the scale factor is its eigenvalue. This concept helps reveal the “core behavior” of a transformation by identifying its natural directions. These ideas show up in many real-world applications. In systems of differential equations, eigenvalues determine stability and long-term behavior. In data science, they are used in techniques like principal component analysis to find the most important directions in data. In physics and engineering, they help describe vibrations, energy states, and dynamic systems. Eigenvalues tell you how strong the effect is in a certain direction, while eigenvectors tell you which directions matter most, making them a powerful tool for simplifying complex systems. Like this video and follow @mathswithmuza for more! #math #physics #matrix #algebra #linear

Proving functions are linearly independent on 🇺🇸 Independence Day 🇺🇸 #math #independent #linearalgebra #diffEQ

Theorem this, matrix that #engineering #engineer #stem #study #studystudy #studystudystudy #college #physics #calculus #algebra #linearalgebra #university

1/1000, equation of the tangent line, calculus 1 #bprp1000

🔢🔄 Sistemas de Ecuaciones Lineales: Tres Perspectivas para un Mismo Concepto 📊 Análisis integrado de su interpretación Este contenido visual presenta tres marcos conceptuales equivalentes para interpretar y resolver un sistema de ecuaciones lineales, explicando cómo cada enfoque revela distintas propiedades estructurales del problema. ▶️ Tres interpretaciones fundamentales: 1. Como sistema de ecuaciones: Un conjunto de ecuaciones que deben satisfacerse simultáneamente. Ejemplo: a₁x + b₁y = c₁ a₂x + b₂y = c₂ 2. Como combinación lineal: Búsqueda de coeficientes (x, y) que, al combinar linealmente vectores columna, produzcan el vector de términos independientes. Esto define el término "lineal": incógnitas elevadas a la primera potencia, sin productos entre ellas. 3. Como producto matricial: Expresión compacta A·X = B. Destaca la estructura algebraica y permite aplicar herramientas del álgebra lineal (determinantes, inversas). 📌 ¿Por qué se denomina "lineal"? · Cada ecuación describe una línea recta (en 2D) o un plano/hiperplano (en dimensiones superiores). · Las operaciones permitidas (suma de incógnitas, multiplicación por escalares) preservan esta geometría rectilínea. · La solución corresponde a la intersección de estos objetos geométricos. ⚙️ Aplicaciones diferenciadas: ➡️ Sistema: Resolución algebraica directa en física e ingeniería. ➡️ Combinación lineal: Análisis de espacios vectoriales en gráficos computacionales. ➡️ Producto matricial: Implementación en algoritmos de machine learning y optimización. 🎯 Dirigido a: Estudiantes y profesionales de álgebra lineal, matemáticas aplicadas, ingenierías y ciencias de datos. 💬 ¿En qué contexto utilizas con mayor frecuencia alguna de estas interpretaciones? Comparte tu enfoque en los comentarios. — Comparte este recurso con quienes busquen una comprensión multidimensional de los sistemas lineales. #maths #mathematics #mathematik #mathematical #linearalgebra #matrix #vectors #university #engeneer #engeneering #epn #uce #aprende #aprendizaje #nivelacion #fypシ❤️💞❤️ #mathidea