In 3D, rotation matrices are used to rotate objects around the x, y, or z axes. Each axis has its own specific rotation matrix. For example, rotating around the z-axis uses a matrix that leaves the z-coordinate unchanged but rotates the x and y coordinates, effectively spinning the object in the xy-plane. Similarly, rotating around the x-axis affects the y and z values, while rotating around the y-axis affects the x and z values. These 3x3 matrices are always orthogonal, meaning their rows and c
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Gurwinder singh on Instagram: "🎥 3D Matrix — When the Determinant is Zero What happens when you apply a 3x3 matrix to space? In this animation: We start with the standard cube formed by the unit vectors î, ĵ, k̂, shown as yellow arrows. These vectors form the edges of a perfect cube. The determinant of the identity matrix is ​​1 → the cube has volume. We then apply a matrix whose determinant is zero. Notice how the cube collapses! The transformed vectors still form a region, but it loses depth:
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Gurwinder singh on Instagram: "🎥 3D Matrix — When the Determinant i…
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∞ ɱ α ƚ ԋ ҽ ɱ α ƚ ι ƈ ʂ ∞ 🇹🇭 on Instagram: "Understanding 3D Linear Transformations (Matrix Multiplication) Start with an input vector v = (x, y, z) ↓ A matrix represents a linear transformation (each column shows where the basis vectors go) ↓ Multiplying a matrix by v = applying the transformation to the vector ↓ If two matrices are multiplied together: A · B ↓ This means: First apply transformation B Then apply transformation A ↓ Order matters! A · B ≠ B · A (in general) ↓ Geometric interpre
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🚀 Day 17 of my machine learning journey! Today we explored transformations between different dimensions, specifically how a 3x2 matrix represents a transformation from 2D to 3D space. 🌐 #linearalgebra #machinelearning #learnontiktok #math
🚀 Day 17 of my machine learning journey! Today we explored transf…
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