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### Lectures on Matrices by J. H. M. Wedderburn

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Matrix Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books. 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

##### Math Books of Matrix Algebra

Matrix Calculus (2nd Edition) by E. Bodewig
• Free
• English
• PDF 103
• Page 450
##### SHORTCUT TRICKS (Division)
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##### Worksheets (Solved)

###### Integration     