Lectures on Matricies(full)

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American Mathematical Society
Colloquium Publications
Volume 17
American Mathematical Society
Providence, Rhode Island
Lectures on Matrices
J. H. M. Wedderburn
	coll17-frnt.pdf
	Frontmatter
	Title
	Preface
	Contents
	Corrigenda
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chI.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	I. Linear transformations and vectors
	2. Linear dependence
	3. Linear vector functions and matrices
	4. Scalar matrices
	5. Powers of a matrix; adjoint matrices
	6. The transverse of a matrix
	7. Bilinear forms
	8. Change of basis
	9. Reciprocal and orthogonal bases
	10. The rank of a matrix
	11. Linear dependence
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chII.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Characteristic Equation
	I. Identities
	2. Matric polynomials in a scalar variable
	3-4. The division transformation
	5-6. The characteristic equation
	7-8. Matrices with distinct roots
	9-12. Matrices with mulitple roots
	13. The square root of a matrix
	14. Reducible matrices
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chIII.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	I. Elementary transformations
	2. The normal form of a matrix
	3. Determinantal and invariant factors
	4. Non-singular linear polynomials
	5. Elementary divisors
	6-7. Matrices with given elementary divisors
	8-9. Invariant vectors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chIV.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	I. Vector polynomials
	2. The degree invariants
	3-4. Elementary sets
	5. Linear elementary bases
	6. Singular linear polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chIX.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	I. Automorphic transformation
	2-3. The equation y' = +/-aya^-1
	4. Principal idempotent and nilpotent elements
	5. The exponential solution
	6. Matrices which admit a given transformation
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chV.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	I. Compound Matrices
	2. The scalar product
	3. Compound matrices
	4. Roots of compound matrices
	5. Bordered determinants
	6-7. The reduction of bilinear forms
	8. Invariant factors
	9. Vector products
	10. The direct product
	11. Induced or power matrices
	12-14. Associated matrices
	15. Transformable systems
	16-17. Transformable linear sets
	18-19. Irreducible transformable sets
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chVI.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	I. Hermitian matrices
	2. The invariant vectors of a hermitian matrix
	3. Unitary and orthogonal matrices
	4. Hermitian and quasi-hermitian forms
	5. Reduction of a quasi-hermitian form 
	6. The Kronecker method of reduction
	7. Cogredient transformation
	8. Real representation of a hermitian matrix
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chVII.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	I. Commutative matrices
	2. Commutative sets of matrices
	3. Rational methods
	4. The direct product
	5. Functions of commutative matrices 
	6. Sylvester's identities
	7. Similar matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chVIII.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	I. Matric polynomials
	2. Infinite series
	3. The canonical form of a function
	4. Roots of 0 and 1
	5-6. The equation y^m = x; algebraic functions
	7. The exponential and logarithmic functions
	8. The canonical form of a matrix in a given field
	9.The absolute value of a matrix
	10. Infinite products
	11. The absolute value of a tensor
	12. Matric functions of a scalar variable
	13. Functions of a variable vector
	14. Functions of a variable matrix
	15-16. Differentiation formulae
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	coll17-chX.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	I. Fields and algebras
	2. Algebras which have a finite basis
	3. The matric representation of an algebra
	4. The calculus of complexes
	5. The direct sum and product 
	6. Invariant subalgebras
	7. Idempotent elements
	8-9. Matric subalgebras
	10-12. The classification of algebras
	13. Semi-invariant subalgebras
	14. The representation of a semi-simple algebra
	15. Group algebras
	Endmatter
	coll17-bck.pdf
	Frontmatter
	Chapter I. Matrices and Vectors
	Chapter II. Algebraic Operations with Matrices. The Charactersitic Equation
	Chapter III. Invariant Factors and Elementary Divisors
	Chapter IV. Vector Polynomials. Singular Matric Polynomials
	Chapter V. Compound Matrices
	Chapter VI. Symmetric, Skew, and Hermitian Matrices
	Chapter VII. Commutative Matrices
	Chapter VIII. Functions of Matrices
	Chapter IX. The Automorphic Transformation of a Bilinear Form
	Chapter X. Linear Associative Algebras
	Endmatter
	Appendix I
	Notes
	Appendix II
	Bibliography
	Index to Bibliography
	Index