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A tensor generalizes vectors and matrices into higher-dimensional mathematical objects that describe relationships between multiple quantities. A vector is a 1D list, a matrix is a 2D grid, and a 3rd order tensor can be visualized as a 3D cube. The stress tensor σᵢⱼ represents internal forces within a material, while the Riemann curvature tensor R(u,v)w = ∇ᵤ∇ᵥw − ∇ᵥ∇ᵤw − ∇₍[u,v]₎w describes the curvature of spacetime in general relativity. Other concepts shown include the product derivative rule, the tensor product A ⊗ B, and the quantum state (1/√2)(|00⟩ + |11⟩). Tensors are indispensable in engineering, physics, machine learning, computer vision, and many other fields where multidimensional data and complex interactions must be modeled accurately.

cosmosarcive's tweet photo. A tensor generalizes vectors and matrices into higher-dimensional mathematical objects that describe relationships between multiple quantities.

A vector is a 1D list, a matrix is a 2D grid, and a 3rd order tensor can be visualized as a 3D cube. The stress tensor σᵢⱼ represents internal forces within a material, while the Riemann curvature tensor

R(u,v)w = ∇ᵤ∇ᵥw − ∇ᵥ∇ᵤw − ∇₍[u,v]₎w

describes the curvature of spacetime in general relativity. Other concepts shown include the product derivative rule, the tensor product A ⊗ B, and the quantum state

(1/√2)(|00⟩ + |11⟩).

Tensors are indispensable in engineering, physics, machine learning, computer vision, and many other fields where multidimensional data and complex interactions must be modeled accurately.

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l9999v9l retweeted

Mathematica

@mathemetica

10 days ago

A single central polyhedron branches into an array of symmetric solids via geometric operations under icosahedral symmetry. Labeled arrows indicate T₂ₑ to the cyan truncated dodecahedron, A_F to the yellow dodecahedron, A_E to the green icosidodecahedron, T₂ᵢ to the purple truncated icosidodecahedron, T_f and T_r to the blue rhombicosidodecahedron, with additional links to the magenta truncated icosahedron and the blue snub dodecahedron. These polyhedra underpin structural models of fullerenes in nanotechnology and icosahedral capsids in virology.