Linear Algebra
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Comprehensive guide to basis and dimension
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3D linear transformations
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Visualizing transformations in 2D and 3D
The geometry of linear algebra Linear algebra is often taught as a mechanical subject; solve for x, invert this matrix, compute that determinant. But beneath the calculation lies a deeply geometric story. One that’s not just useful for understanding the math but essential for remembering it. This post is a guide to seeing what linear…
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Adding and subtracting vectors made simple
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Understanding linear transformations intuitively
Matrices as Machines Most people first encounter matrices as lifeless grids, rows, and columns filled with numbers. The rules for working with them seem arbitrary. Multiply this row by that column. Follow this sequence. Don’t ask why. But there’s a far more intuitive, visual way to understand what’s going on. A matrix is a machine.…
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One more time: What is Linear Algebra
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Avoiding Redundancy: Linear Independence
(or: Why packing two hairdryers is a terrible idea) Picture this: you’re packing for a short trip. You double-check your bag, and, just to be safe, you toss in two identical hairdryers. Same size, same model, same everything. Unless you’re secretly a stylist on tour, that second hairdryer? Pointless. It adds weight without adding value.…
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Vectors: The Building Blocks of Linear Algebra
Picture giving directions: “Take 3 steps forward, then 4 to the right.” That’s a vector, a quantity with both direction and magnitude. In math, it’s written like this:v = [3, 4] This notation shows how far to move in each dimension. It’s concise, practical, and powerful. Vectors appear in physics (forces), video games (movement), data…
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Linear Algebra
Welcome to a new set of blog posts that will explore Linear algebra. At its core, linear algebra is a branch of mathematics that deals with: Vectors: These are quantities that have both a magnitude and a direction, like arrows. Vector Spaces: These are sets of vectors that follow certain rules. You can add vectors…