This site contains a tool that uses the Gram-Schmidt orthonormalization process to compute the orthonormal basis once an arbitrary basis in a Euclidean space is entered.
Type of Material:
Simulation
Recommended Uses:
This site can be used in class, at home, or for individual and learning.
Technical Requirements:
Any Internet browser
Identify Major Learning Goals:
To apply and view the Gram-Schmidt process
Target Student Population:
Students in a Linear Algebra class.
Prerequisite Knowledge or Skills:
Introductory Linear algebra.
Content Quality
Rating:
Strengths:
The Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space. The Gram–Schmidt process takes a finite, linearly independent set and generates an orthonormal set that spans the same subspace.
The user chooses the dimension of the Euclidean space, types entries into the relevant vectors, and then clicks on the “Submit” button. The output appears on a new page and consists of all three steps of G-S process (original-orthogonal-orthonormal). The applet also computes the corresponding orthogonal matrix. The output is given to six decimal place accuracy.
Concerns:
The Gram–Schmidt process is meant to be run on a linearly independent set of vectors. If a linearly dependent set of vectors is entered, the applet issue no warning and still runs producing not basis sets, even if all vectors are the zero vector.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The applet efficiently carries out a computation which would be hard to do by hand. A user can adjust the dimension of the space (and number of vectors) up to six dimensions. Producing (as mentioned above) all the steps of the method is an advantage compared to a standard computer algebra system.
The applet can be used as an aid to a lecture or as a quick in-class demonstration.
Concerns:
Classroom activities will be slowed down by the time needed to enter the original vectors term-by-term. (This is probably unavoidable in matrix computations, though.)
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The module under review is straight-forward and intuitive. The applet has only one button found and is very easy to use. The average user can begin using the applet immediately.
Concerns:
The site could certainly benefit from the presence of basic navigation buttons and a link to more information on the Gram-Schmidt process.
Creative Commons:
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