Linear Algebra Index

(alphabetized)

• Injective, Surjective, Invertible equivalences
• A Linear Transformation Is Determined By How It Acts On A Basis
• A Matrix Is Diagonalizable If And Only If There Is An Eigenvector Basis
• Augmented Matrix
• Basis Change
• Basis For A Direct Sum
• Basis Of Product Of Basis Change Matrix And Vector
• Basis
• Cayley Hamilton Theorem
• Characteristic Polynomial
• Column And Row Space
• Combination Of Basis Change
• Condition For Bijective Matrix Transformation
• Condition For Diagonalizable
• Condition For Row Equivalence
• Conditions For Injective Transformation
• Coordinate Vector
• Determinant
• Diagonalizable
• Dimension Of Row And Column Space
• Dimension Of Subspace
• Dimensions
• Direct Sum
• Direct Sums Decomposes Into Families Of Projections
• Eigenspace
• Eigenvalue
• Eigenvector
• Eigenvectors And Determinants
• Elementary
• Elements Of A Span
• Equivalent Systems Have The Same Solution
• Equivalent
• Every Linear Transformation Can Be Represented By A Matrix
• Every Matrix Is Row Equivalent To A Row Reduced Matrix
• Every Vector Space Has A Basis
• Existance Of Basis
• Existance Of Minimal Polynomial
• Free Variables
• Homogeneous
• Ideal
• Idenpotent
• If A Has A Left And Right Inverse Then It Is Invertible With A Unique Inverse
• Condition for Square Matrices to have an Unique Solution
• If E Is An Elementary Matrix Then Ea Is The Matrix Obtained By Applying The Elementary Row Op That Defies E To A
• If T Has N Distinct Eigenvalues Then It Is Diagonalizable
• If V And W Are Finite Dimensional Vector Spaces Then Space Of Linear Transformations Is A Vector Space
• If M Is Greater Then N For A Mxn Matrix Then Ax Equals 0 Has A Nontrivial Solution
• Independent
• Injective And Surjective Conditions
• Intersection Of Subspaces
• Invarient
• Inverse Matrix
• Invertible Equivalences
• Invertible
• Isomorphism
• Linear Combination
• Linear Dependent And Independent
• Linear Transformation
• Matrix Multiplication Is Associative
• Matrix Multiplication
• Matrix Of A Linear Transformation
• Matrix Representation
• Minimal Polynomial
• Non Trivial Solutions For A Mxn Matrix
• Nonhomgenous
• Number Of Elements In A Linearly Independent Set
• Over Algebraically Compete Fields The Determineant Is Product Of Eigenvalues And Trace Is The Sum Of Eigenvalues
• Properties Of Invertible Matrices
• Rank Nullity Theorem
• Rank Of A Matrix And Its Transpose
• Roots Of Minimal Polynomials Are Eigenvalues
• Row Equivalent Matrices Have The Same Solution
• Row Equivalent
• Row Reduced Echelon
• Row Reduced
• Similar
• Size Of Basis
• Skew Symmetric
• Space Of Linear Transformations
• Span
• Squares And Square Roots
• Subsets With More Or Less Vectors Than Dimensions
• Subspace
• Sum Of Subspaces
• Symmetric
• The Determinant Is Multiplicative
• The Determinant Is Well Defined
• The Determinant Is Zero If And Only If The Set Is Linearly Dependent
• The Determinant Of A Matrix Times An Elementary Matrix Is The Product Of The Determinants
• The Matrix Representation Of A Transformation In Different Basis Are Similar
• The Set Of Matrices With Addition And Multiplication Form A Ring
• There Exists A Basis Such That A Matrix Is Upper Triangular
• Transpose
• Unipotent
• Upper Triangular
• Vector Space
• Vector