Matrix function

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/matrix-function

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is a matrix function?A matrix function takes a whole matrix and turns it into another matrix, just like a normal function turns a number into another number.
2. How do we calculate a matrix function using a power series?If the function can be written as a sum of powers, we replace each power of the number with a power of the matrix, multiply the matrix by itself the needed number of times, and add all the results together.

Analytic Function: A function that can be represented by a convergent power series in a neighborhood of each point.
Spectral Decomposition: Representing a matrix in terms of its eigenvalues and eigenvectors.
Jordan Normal Form: A canonical form for a square matrix, useful for theoretical analysis of matrix functions.