Matrix vocabulary

Learning Objectives Define a matrix and state its dimensions (order). Identify the rows, columns, and specific elements of a matrix using standard notation (e.g., a_ij). Distinguish between different types of matrices, including row, column, square, zero, and identity matrices. Define and identify the main diagonal of a square matrix. Determine if two matrices are equal by comparing their dimensions and corresponding elements. Find the transpose of a given matrix. Ever wonder how a computer program can instantly apply a photo filter or how video games render complex 3D worlds? 🎮 It all starts with organizing data in a grid, which is exactly what a matrix is! This tutorial introduces the fundamental vocabulary used to describe matrices. Understanding these core terms is the...

TermDefinitionExample MatrixA rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are typically enclosed in square brackets or parentheses.A = \begin{bmatrix} 5 & -2 & 0 \\ 1 & 4 & 7 \end{bmatrix} is a matrix with 2 rows and 3 columns. Dimensions (or Order)The size of a matrix, expressed as the number of rows by the number of columns (rows × columns).The matrix B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} has dimensions 3 × 2 because it has 3 rows and 2 columns. Element (or Entry)Each individual value within a matrix. An element's position is identified by its row and column number.In the matrix C = \begin{bmatrix} 9 & 8 \\ 7 & 6 \end{bmatrix}, the number 7 is an element located in the 2nd row...

Element Notation a_{ij} This notation is used to specify the element in the i-th row and j-th column of a matrix A. The row index 'i' always comes before the column index 'j'. Matrix Equality A = B \text{ if and only if } a_{ij} = b_{ij} \text{ for all } i, j Two matrices, A and B, are considered equal only if they have the exact same dimensions AND every element in matrix A is equal to the corresponding element in matrix B. Transpose Dimensions \text{If A is an } m \times n \text{ matrix, then } A^T \text{ is an } n \times m \text{ matrix.} When you find the transpose of a matrix, the number of rows and columns are swapped. The dimensions are effectively flipped.