San Diego Connections of Eigenvectors & Eigenvalues Determinant Trace Diagonalizing of A Matrix

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Gerfbznorpx

Mathematics

University of San Diego

Description

Recent Concepts:

For this assignment, you will write a document explaining the connections between the following course concepts:

. Eigenvectors and eigenvalues

. Determinant of a matrix

. Trace of a matrix

. Diagonalizing a matrix

. Matrix has / does not have basis of eigenvectors

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Explanation & Answer

Hello, I'm done, all parts ar correctly answered as per the instructions.

Running head: CONCEPTUAL ASSIGNMENT

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Conceptual Assignment
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CONCEPTUAL ASSIGNMENT

Conceptual Assignment
The basics that form the heart of computing and mathematics are the central core of the
field of data science. What they are. How they are computed and how they applied is a theme that
everyone may want to know in-depth. This assignment will discuss the connections between
concepts such as Eigenvectors and eigenvalues, Determinant of a matrix, Trace of a matrix,
Diagonalizing a matrix, Matrix has/does not have the basis of eigenvectors.

Eigenvectors and eigenvalues
Scientists have to input data from several sources when they want to build equations or
mathematical models. The first step is to find which variable is depended on which variable (e.g.,
Interest rate/time, such that interest rate y, is depended on x). Gathering of data will use one-hot
encoding to transform data values, which may be in a textual format to numeral matrices. Next is
to converge the data into tables forming matrices.
However, this model may take a lot of disk space and time consuming to calculate and
visualize a data set of more than 100+ dimensions. Eigenvectors and eigenvalues come in to
compress that data to intensive computable values that eliminate problems of huge data sets. For
instance; consider bob’s house location coordinates [10, 10], let this be vector A[X=10, Y=10].
Again, Alex lives in a house coordinates [20, 20], this to be matrix B [20, 20]. If bob wants
to meet Alex, he has to travel 10 points on the X and 10 points on the Y-axis. Thus the magnitude
would form vector C [10, 10]. Before defining the terms, .it is important to note that a twodimensional vector contains magnitude and direction.
Again, we can transform matrices by multiply matrix A with matrix B. this new
transformed vector means it can be computed by multiplying a scalar to the original vector.

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CONCEPTUAL ASSIGNMENT

Therefore, an eigenvector of the original Matrix occurs when a scalar has produced the transformed
Matrix to the original Matrix. Eigenvectors are special vectors with special characteristics. If our
input is large sparse matrix M can find a vector, O to replace the large Matrix by multiplying the
scalar and the vector, O. [M * o = n...


Anonymous
Really great stuff, couldn't ask for more.

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