Definitions and Theorems 3

Thursday, April 12, 2012

1:39 PM

Chapter 5

 Right Inverse Left inverse

Theorem 5.1.1

Corollary 5.1.2

Theorem 5.1.3

 Matrix Inverse Invertible

Theorem 5.1.4

Theorem 5.1.5

Theorem 5.1.6

Theorem 5.1.7 (Invertible Matrix Theorem)

 Elementary Matrix

Theorem 5.2.1.

Theorem 5.2.2

Theorem 5.2.3

Theorem 5.2.4

Theorem 5.2.5

Corollary 5.2.6

Theorem 5.2.7

 Cofactor

Theorem 5.3.1

 Upper Triangular Lower triangular

Theorem 5.3.2

Theorem 5.3.3

Theorem 5.3.4

Corollary 5.3.5

Theorem 5.3.6

Corollary 5.3.7

Theorem 5.3.8 (Addition to the Invertible Matrix Theorem)

Theorem 5.3.9

Corollary 5.3.10

Theorem  5.3.11

Lemma 5.4.1

Theorem 5.4.2

Theorem 5.4.3 (Cramer's Rule)

 Area of a parallelogram Height of Parallelepiped Volume of Parallelepiped

Chapter 6 - Diagonalization

 It satisfies Diagonal Matrix

Theorem 6.1.1

Then

 Trace

 Similar Matrices

 Eigenvalue Eigenvector Eigenpair Eigenvalues Eigenvectors

 Characteristic Polynomial

Theorem 6.2.1

 Eigenspace

 Algebraic Multiplicity Geometric Multiplicity

Lemma 6.2.2

Theorem 6.2.3

 Diagonalizable

Theorem 6.3.1

Theorem 6.3.2

Corollary 6.3.3

 Deficient

Corollary 6.3.4

Theorem 6.3.5

Then

Theorem 6.4.1

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