7/25/2019 Topics in a Linear Algebra Course.docx

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Topics in a Linear AlgebraCourse

To learn more about a topic listed below, click the topic name to go tothe corresponding MathWorldclassroom page.

Eigenvalue

One of a set of special scalarsassociated with a linear system ofequations that describes that system'sfundamental modes. An eigenvector isassociated with each eigenvalue.

Eigenvector

One of a special set of vectorsassociated with a linear system ofequations. An eigenvalue is associatedwith each eigenvector.

Euclidean pace

The space of all n!tuples of realnumbers. "t is the generali#ation of thetwo dimensional plane and threedimensional space.

"nner $roduct

%& "n a vector space, a way to multiplyvectors together, with the result of thismultiplication being a scalar. %( Asynonym for dot product.

)inear Algebra

The study of linear systems of equations

and their transformation properties.

)inear Transformation

A function from one vector space toanother. "f bases are chosen for thevector spaces, a linear transformationcan be given by a matri*.

+atri* A concise and useful way of uniquelyrepresenting and working with lineartransformations. "n particular, for everylinear transformation, there e*ists e*actly

one corresponding matri*, and everymatri* corresponds to a unique lineartransformation. The matri* is ane*tremely important concept in linearalgebra.

+atri* "nverseiven a matri* M, the inverse is a newmatri* M!&that when multiplied by M,gives the identity matri*.

+atri* +ultiplication

The process of multiplying two matrices%each of which represents a lineartransformation, which forms a newmatri* corresponding to the matri*representation of the twotransformations' composition.

-ormA quantity that describes the length, si#e,

or e*tent of a mathematical obect.

/ector pace

A set that is closed under finite vectoraddition and scalar multiplication. Thebasic e*ample is n!dimensionalEuclidean space.

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