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Lectures on Matrices by J. H. M. Wedderburn


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Lectures on Matrices written by J. H. M. Wedderburn American Mathematical Society, Providence, Rhode Island BEETION. This is an other great mathematics book cover the following topics.

  • 1. MATRICES AND VECTORS
    1. 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. Bilinearforms
    8. Change of basis
    9. Reciprocal and orthogonal bases
    10. The rank of a matrix
    11. Linear dependence

  • 2. ALGEBRAIC OPERATION8 WITH MATRICES . THE CHARACTERISTIC EQUATION
    1. Identities
    2. Matric polynomials in a scalar variable
    5-6. The characteriatic equation
    7-8. Matricer with distinct rootr
    4-12. Matrices with multiple roots
    13. The square root of a matrix
    14. Reducible matrices

  • 3. INVARIANT FACTORB AND ELEMENTARY DIVISORS
    1. 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

  • 4. VECTOR POLYNOMIALS
    1. SINGULAR MATRIC POLYNOMIALS
    2. Vector polynomials
    3. The degree invariants
    4. Elementary sets
    5. Linear elementary bases
    6. Singular linear polynomials

  • 5. COMPOUSD MATRICES
    1. 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

  • 6. SYMMETRIC. SKEW. AND HERMITIAN MATRICES
    1. 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 to the sum of squares
    6. The Kronecker method of reduction
    7. Cogredient transformation
    8. Real representation of a hermitian matrix

  • 7. COMMUTATIVE MATRICES
    1. 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

  • 8. FUNCTIONS OF MATRICES
    1. Matric polynomials
    2. Infinite series
    3. The canonical form of a function
    4. Roots of 0 and 1
    5-6. The equation ym = 2; 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. hlatric functions of a scalar variable
    13. Functions of a variable vector
    14. Functions of a variable matrix
    15-16. Differentiation formulae

  • 9. THE AUTOMORPHIC TRANSFORMATION OF A BILINEAR FORM
    1. 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

  • 10. LINEAR ASSOCIATIVE ALGEBRAS
    1. Fields and algebras
    2. Algebra$ 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. bIatric subalgebras
    10-12. The classification of algebras
    13. Semi-invariant subalgebras
    14. The representation of a semi-simple algebra
    15. Group algebras

  • Notes

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