Math 141 Final Exam Definitions Review

LU Gaussian Elimination

Echelon Form

Pivot

Rank

Augmented Matrix

Back-substitution

Vector Addition

Scalar Multiplication

Matrix-vector equation

Linear combination

Column picture

Row picture

Span

Subspace

Linear Independence

Trivial Solution

Basis

Dimension

Homogeneous System

Nullspace

Column Space

Row Space

Left Nullspace

Complete Solution

Identity matrix

Linear Transformation

Kernel

Range

Injective

Surjective

Bijective

Dot product

Orthogonal Projection

Projection

Inverse

Determinant (Computational)

Determinant (Volume)

Determinant (Linear Transformation)

Orthogonal subspaces

Orthogonal Compliment

Schwarz inequality

Triangle Inequality

Projection matrix

Orthonormal

Orthogonal matrix

Gram-Schmidt process

Eigenvalue/Eigenvector

Eigenspace

Algebraic Multiplicity

Geometric Multiplicity

Similar Matrices

Diagonalization

Change of basis matrix

Symmetric Matrix

Positive Definite Matrix

Singular Value Decomposition

Fundamental Theorem Of Linear Algebra Part 1

Fundamental Theorem of Linear Algebra Part 2