Matrix Notation & Structure

Linear Algebra for Machine Learning · Axiom Academy

The Language of Rows, Columns, and Entries Matrix notation is the standardized way to write matrices. It allows us to write complex data in a compact form and communicate precisely about which elements we're referring to. Let's learn the language. A matrix is a rectangular arrangement of numbers. We often denote matrices with capital letters like A, B, or M. The numbers inside are called entries or elements . The dimensions (or order ) of a matrix tell us its size. A matrix with m rows and n columns is said to be an m × n matrix (read "m by n"). In this example above, we have 3 rows and 4 columns, so it's a 3×4 matrix. Each entry in a matrix is identified by its position. We write aᵢⱼ to mean the entry in row i and column j . For example, a₂₃ means the entry in row 2, column 3 (which is 7 in the matrix above). Some matrices have special forms that appear frequently. Learn to recognize them: Number of rows equals number of columns. An n×n matrix. Square matrix with 1s on the diagonal, 0s elsewhere. Written as I. Only diagonal entries are nonzero. All other entries are 0. All entries are 0. Often written as 0 or O. A matrix with only one column. Also called n×1 matrix. A matrix with only one row. Also called 1×n matrix. Follow these conventions when working with matrices: Practice Understanding Notation Exercise: For the matrix A shown below, what is a₁₃? What are the dimensions? Answer: a₁₃ = 2, dimensions are 2×3

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