Linear Algebra
Class 12

Matrix Addition

[A+B]ij=aij+bij[A+B]_{ij} = a_{ij} + b_{ij}
024681005101520
[A+B]ᵢⱼ = aᵢⱼ + bᵢⱼ

Adjust Variables

Matrix size n
n =
25

Matrices of same dimensions are added element by element. Order doesn't matter (commutative).

Real-World Applications

Image processing — Adding images (overlays, blending).

Social networks — Combining adjacency matrices.

Economics — Adding input-output matrices.

Physics — Superposition of wave amplitudes.

Data science — Combining feature matrices.

Computer graphics — Combining transformation effects.

Statistics — Adding covariance matrices.

Engineering — Combining stress matrices.

Finance — Portfolio aggregation.

Robotics — Combining sensor readings.

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