Matrices Lecture Notes

Flashcards covering key concepts and definitions related to matrices.

What is a matrix?

An array of numbers organized into rows and columns.

Order of a matrix

The size of a matrix defined by the number of rows and columns.

Matrix Addition and Subtraction

Matrices must be of the same order to add or subtract elements in the same position.

Scalar multiplication

Multiplying each element of a matrix by the same number.

Condition for multiplying matrices

Matrices A and B can be multiplied if the number of columns in A equals the number of rows in B.

Resulting order of a matrix multiplication

The resulting matrix's order is defined by the number of rows from the first matrix and the number of columns from the second matrix.

Identity matrix

A square matrix where all diagonal entries are 1 and all other elements are 0.

Determinant

A value calculated for a square matrix, representing the product of its leading diagonal minus the product of its trailing diagonal.

Inverse matrix

A matrix that, when multiplied with the original matrix, yields the identity matrix.

Singular matrix

A matrix that has no inverse, typically because its determinant is zero.

Commutative property of matrix multiplication

Matrix multiplication is not commutative, meaning AB does not necessarily equal BA.

Matrix multiplication example

The process of multiplying two matrices involves each row of the first matrix being multiplied by each column of the second.