Mathematics
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How linear algebra powers AI, physics, and cryptography
When most people hear the term linear algebra, they imagine rows of numbers in matrices or tedious exercises with vectors. Yet, far from being an isolated branch of mathematics, linear algebra is the hidden architecture of modern science and technology. It is the language that allows people to describe relationships, transformations, and patterns in systems…
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Orthogonal and Orthonormal vectors
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How to calculate eigenvectors?
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Understanding eigenvectors and eigenvalues
At first glance, words like eigenvector and eigenvalue look like they belong in some obscure math museum. But behind the heavy names are surprisingly simple ideas. They’re not about memorising formulas. They’re about uncovering the hidden rules that shape change: in geometry, in data, and even across the internet. Impact-Site-Verification: bc51445e-155a-462e-ac33-1e505feb70af Rubber sheets and secret…
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Inverse of a matrix
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The power of the inverse
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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