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Matrix Operations
High School
Definition
Operations on matrices: addition, scalar multiplication, matrix multiplication.
Formulas
(A + B)_ij = A_ij + B_ij
Matrix addition (same dimensions)
(cA)_ij = c · A_ij
Scalar multiplication
(AB)_ij = ∑_k=1ⁿ A_ikB_kj
Matrix multiplication (A: m×n, B: n×p → AB: m×p)
Examples
Example 1
Find AB where A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]].
Applications
Computer Graphics
Composition of transformations
Neural Networks
Layer computations
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