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Student[LinearAlgebra][EigenvaluesTutor] - interactive and step-by-step matrix eigenvalues

Calling Sequence

EigenvaluesTutor(M, opts)




square Matrix



(optional) equation(s) of the form option=value where equation is output or displaystyle



The EigenvaluesTutor(M) command by default opens a Maplet window which allows you to work interactively through solving for the eigenvalues of M. Options provide other ways to show the step-by-step solutions, as described below.


The EigenvaluesTutor(M) command presents the techniques used in finding the eigenvalues of the square matrix M by:


Creating the matrix M - lambda*Id where Id is an identity matrix with dimensions equal to that of M


Taking the determinant of M - lambda*Id


Finding the roots of the resulting characteristic polynomial


The Matrix M must be square and of dimension 4 at most.


Floating-point numbers in M are converted to rationals before computation begins.


If the symbolic expression representing an eigenvalue grows too large, then the value displayed in the Maplet application window is a floating-point approximation to it (obtained by applying evalf).  The underlying computations continue to be performed using exact arithmetic, however.


The EigenvaluesTutor(M) command returns the eigenvalues as a column Vector.


The following options can be used to control how the problem is displayed and what output is returned, giving the ability to generate step-by-step solutions directly without going through the Maplet tutor interface:


output = steps,canvas,script,record,list,print,printf,typeset,link (default: maplet)

The output options are described in Student:-Basics:-OutputStepsRecord.  Use output = steps to get the default settings for displaying step-by-step solution output.


displaystyle= columns,compact,linear,brief (default: linear)

The displaystyle options are described in Student:-Basics:-OutputStepsRecord.  








Compute the Eigenvalues120232021Calculate A=M-t*Id1t2023t2021tFind the determinant; this is also called the characteristic polynomial of M.Use cofactor expansion on the3by3matrix1t3t221t+−122201t+1023t02Find the determinant of the 2 by 2 matrices by multiplying the diagonals1t3t1t22+−1221t02+102203tEvaluate inside the brackets1t3t1t4+−1222t+104Multiply1t3t1t4+4+4t+0Evaluate1t3t1t44+4tFind the determinant; this is also called the characteristic polynomial of M.t3+5t2+t5Solve; the eigenvalues are the roots of the characteristic polynomial.51−1


See Also

factor, Student[LinearAlgebra], Student[LinearAlgebra][Determinant], Student[LinearAlgebra][Eigenvalues], Student[LinearAlgebra][EigenvectorsTutor]