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Glossary

Look up any term from this course. Each entry links back to the lesson that taught it.

Glossary of course terms
Term	Definition	Lesson
3×3 determinant	$Expand along the first row with signs + - +: each entry times its 2 \times 2 minor.$	The Determinant of a 3×3 Matrix
Area scale factor	$How much a transformation multiplies area by: \|det(M)\| for a transformation matrix M.$	Area Scale Factor and the Determinant
Combined transformation	$Applying two transformations in sequence, equivalent to multiplying their matrices together (second transformation's matrix on the left).$	Enlargement and Combined Transformations
Determinant	$For A = (a c b d), det(A) = ad - bc — a single number revealing key properties of A.$	The Determinant of a 2×2 Matrix
Enlargement (scaling) matrix	$The matrix (k 0 0 k), which scales every point by factor k from the origin.$	Enlargement and Combined Transformations
Identity matrix	$The matrix (1001), which leaves any matrix unchanged under multiplication.$	The Identity Matrix
Inverse matrix	$For A with det(A) \neq 0, A^{- 1} = (1 \div det(A)) \times (d - c - b a) — a matrix that undoes A.$	The Inverse of a 2×2 Matrix
Matrix	$A rectangular array of numbers arranged in rows and columns.$	What Is a Matrix?
Matrix equation (AX = B)	$A way of writing simultaneous equations as a single matrix equation, solved with X = A⁻¹B.$	Solving Simultaneous Equations With Matrices
Matrix multiplication	$Combining rows of the first matrix with columns of the second: multiply pairs, then add.$	Matrix Multiplication
Order of a matrix	$The size of a matrix, written as rows \times columns.$	What Is a Matrix?
Reflection matrix	$A matrix that reflects points in a line, such as (10 0 - 1) for reflection in the x -axis.$	Reflection and Rotation Matrices
Rotation matrix	$A matrix that rotates points about the origin by a fixed angle, such as (01 - 1 0) for 90 ° anticlockwise.$	Reflection and Rotation Matrices
Scalar multiplication	$Multiplying every element of a matrix by the same single number.$	Scalar Multiplication
Singular matrix	$A matrix with determinant 0, which cannot be inverted.$	Singular Matrices
Transformation matrix	$A matrix that, multiplied by a point, produces a transformed point — a reflection, rotation, or enlargement.$	Introduction to Matrix Transformations