Basic Matrix Operations

Linear Algebra for Machine Learning · Axiom Academy

Addition, Scalar Multiplication & Transpose Matrix Operations Fundamentals Just like numbers, matrices can be added, multiplied by scalars, and transformed. Let's master the basic operations. Two matrices of the same dimensions can be added by adding corresponding entries. Matrix addition follows these properties: Multiply every entry in a matrix by a scalar (constant) c. Properties of Scalar Multiplication The transpose of a matrix A, written Aᵀ, is obtained by swapping rows and columns. Row i becomes column i. Example: Compute 2A + 3B where Remember: Matrices must have compatible dimensions for addition. For scalar multiplication, there's no restriction on the matrix size.

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