lightbulb Key Concepts

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1. Addition and Subtraction

Two matrices can be added or subtracted only if they have the same order. Addition is performed element-wise.

2. Scalar Multiplication

Multiplying a matrix by a scalar k involves multiplying every element of the matrix by k.

3. Matrix Multiplication

The product of matrices A (m×n) and B (n×p) is a matrix C (m×p). Matrix multiplication is not commutative (AB ≠ BA in general).

4. Transpose of a Matrix

Obtained by interchanging rows and columns. Property: (AB)ᵀ = BᵀAᵀ.