Linear algebra

linear algebra
Cramer – 1704 – 1752.
Cramer published
Cramer’s rule in 1750 – a method for solving simult. equations.
linear algebra
Gauss – 1777 – 1855.
The man after whom Gaussian elimination is named. We will cover this in section 5.
linear algebra
Sylvester – 1814 – 1897.
In 1848 Sylvester coined the term “matrix”, which is Latin for womb.
linear algebra
Cayley – 1821 – 1895.
In 1856 Cayley introduced the method of matrix multiplication and the matrix inverse.
linear algebra
Peano – 1858 – 1932.
In 1888 Peano was the first to give the modern day definition of the term vector space.

Welcome to the linear algebra page. Here we will explore topics such as vector spaces, linear maps, elementary operations, Gaussian elimination and its role in solving simultaneous equations and more. The course is divided up into sections which you can find below. Within each section, you will find theory along with exercises and their full (hopefully correct) solutions.

If there are any other topics you would like to see included, please email me (email found in the footer).

Course currently under construction.

Contents

Section 1Vectors and vector spaces.
Section 2Spanning, linear independence and bases.
Section 3Column vectors are coordinate vectors.
Section 4Linear maps, their associated matrices, and the rank-nullity theorem.
Section 5Simultaneous equations, Gaussian elimination, and row echelon form.
Section 6Change of basis, change of basis matrices and their effects on linear maps.
Section 7Eigenvalues and eigenvectors.
Section 8Jordan normal form of a matrix.
Section 9Inner products, orthogonality and Gram-Schmidt.
Section 10Determinants and traces.

More linear algebra resources.

If you would like to learn more or see other explanations of the topics discussed above, some places you could look are:

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