Matrices and Their Properties

Flashcards highlighting key vocabulary related to matrices, their properties, operations, and transformations.

Determinant

A scalar value that is computed from the elements of a square matrix, which can be used to determine if the matrix has an inverse.

Inverse Matrix

A matrix that, when multiplied by the original matrix, yields the identity matrix; denoted as M^{-1}.

Orthogonal Matrix

A square matrix whose transpose is equal to its inverse; the condition |M| = ±1 must be satisfied.

Singular Matrix

A matrix that does not have an inverse, typically because its determinant is zero.

Matrix Transpose (MT)

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

Transformation

A function that maps a set of points to another set, commonly used for manipulating the coordinates in geometry.

Scale Factor

A number that scales or multiplies the dimensions of a shape in a transformation, such as enlarging or reducing.

Reflection

A transformation that flips a shape across a line, creating a mirror image.

Rotation

A transformation that turns a shape around a fixed point at a specified angle.

Simultaneous Equations

A set of equations that have common variables, solved together to find the values of those variables.