Matrices

Flashcards covering key concepts, definitions, and properties related to matrices.

Matrix

An ordered rectangular array of numbers or functions.

Order of a matrix

A matrix having m rows and n columns is called an m × n matrix.

Column Matrix

A matrix with only one column; represented as [aij]m × 1.

Row Matrix

A matrix with only one row; represented as [aij]1 × n.

Square Matrix

A matrix where the number of rows equals the number of columns.

Diagonal Matrix

A square matrix in which all non-diagonal elements are zero.

Scalar Matrix

A diagonal matrix in which all diagonal elements are equal.

Identity Matrix

A square matrix in which all diagonal elements are 1 and all non-diagonal elements are 0.

Zero Matrix

A matrix in which all of its elements are zero.

Equality of Matrices

Two matrices are equal if they are of the same order and each corresponding element is equal.

Transpose of a Matrix

The matrix obtained by interchanging the rows and columns of the original matrix.

Symmetric Matrix

A square matrix A is symmetric if A' = A.

Skew Symmetric Matrix

A square matrix A is skew symmetric if A' = -A.

Inverse Matrix

If A is a square matrix, B is its inverse if AB = BA = I.

Properties of Matrix Addition

Matrix addition is commutative and associative, and the zero matrix is the additive identity.

Properties of Matrix Multiplication

Matrix multiplication is associative but not commutative; (AB)C = A(BC) but AB ≠ BA in general.

Determining Matrix Types

It includes diagonal matrices, scalar matrices, identity matrices, and zero matrices.

Matrix Operations

Involves addition, subtraction, and multiplication of matrices.

Matrix Representation in Applications

Matrices are used in various applications like physics, economics, and computer science.