Student[LinearAlgebra][EigenvaluesTutor] - interactive and step-by-step matrix eigenvalues
(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.
M ≔ 1,2,0|2,3,2|0,2,1
Compute the Eigenvalues120232021•Calculate A=M-t*Id1−t2023−t2021−t▫Find the determinant; this is also called the characteristic polynomial of M.◦Use cofactor expansion on the3by3matrix◦Find the determinant of the 2 by 2 matrices by multiplying the diagonals◦Evaluate inside the brackets◦Multiply◦Evaluate−5Find the determinant; this is also called the characteristic polynomial of M.−t3+5⁢t2+t−5•Solve; the eigenvalues are the roots of the characteristic polynomial.51−1
factor, Student[LinearAlgebra], Student[LinearAlgebra][Determinant], Student[LinearAlgebra][Eigenvalues], Student[LinearAlgebra][EigenvectorsTutor]
The Student[LinearAlgebra][EigenvaluesTutor] command was updated in Maple 2021.
The output and displaystyle options were introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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