Linear Algebra - Mind Map

Linear Algebra

Systems of Linear Equations

Linear Combinations

Existence & Uniqueness of Solutions

Inner Product

Orthogonality

Matrices

Linear Transformations

Span

Linear Independence

Subspace

Basis

Dimension

Distance

Orthogonal Set

Orthonormal Set

Orthonormal Basis

Orthogonal Complement

Orthogonal Projection

Orthogonal Matrix

Orthogonal Basis

Best Approximation

Least-Squares

Eigenvector

Length

Eigenvalue

Determinant

Characteristic Polynomial

Transpose

Rank

Nullity (dim Nul)

Rank Theorem

Diagonalizability

Orthogonal Diagonalizability

Symmetric Matrices

Eigenspace

Column Space

Null Space

Eigenvector Basis

Onto

One-to-One

Pivots in Rows

Pivots in Columns

Algebraic Multiplicity

Geometric Multiplicity (dim Eigenspace)

Right Invertibility

Left Invertibility

Invertibility

Existence of Solutions

Uniqueness of Solutions

Nonhomogeneous Systems

Homogeneous Systems

Classification

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