math 141 all definitions

LU Gaussian

Upper Echelon

Pivot

Rank

Augmented Matrix

Matrix vector equation

Back Substitution

Vector Addition

Scalar Multiplication

Linear Combination

Column Picture

Row Picture

Span

Subspace

Linear Independence

Trivial Solution

Basis

Dimensiobn

Homogenous System

Nullspace

Column Space

Transpose

Row Space

Left Nullspace

Complete Solution

Identity Matrix

Linear Transformation

Kernal

Range

Injective

Surjective

Bijective

Dor (or inner) product

Norm

Orthogonal Projection

Projection

Inverse of a linear transformation

Inverse Matrix

Gauss-Jordan method to compute in inverse matrices

Determinant (computational)

Determinant (volume)

Determinant (linear transformation)

Orthogonal subspaces

Orthogonal complement

Schwarz Inequality

Triangle inequality

Projection matrix

Orthonormal

Orthogonal matrix

Gram-Schmidt

Eigenvalue / Eigenvector

Eigenspace

Algebraic Multiplicity

Geometric Multiplicity

Similar Matrices

Diagonalization

Change of basis matrix

Nullspace
Left Nullspace

Fundemental Theorem of Linear Algebra (part 2)
1) The ____ is the orthogonal compliment to the rowspace in Rⁿ
2) The ____ is the orthogonal compliment to the column space in Rⁿ.

Positive (semi) definite matrix

Symmetric Matrix

Singular Value Decomposition