Tag Archives: Linear Algebra

AoPS Question on simultaneous linear equation where coefficients are square numbers

Posted on August 14, 2023 by Sumant Sumant

Assume that are real numbers such that What’s the value of ?

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Distance between point and a plane (direct formula)

Posted on December 20, 2022 by Sumant Sumant
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if A^2 is invertible then A is also invertible

Posted on August 24, 2015 by Sumant Sumant

Saw this question at stack exchange. The proof is easy and I like these two versions is invertible which means . But and so hence is invertible The other proof was let be the inverse of which means which means … Continue reading →

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Linear Algebra Done Right

Posted on May 16, 2015 by Sumant Sumant

Chapter 10: Trace and Determinant (Page 295-332) Chapter 9: Operations on Real Vector Spaces (Page 275-294) Chapter 8: Operators on Complex Vector Spaces (Page 241-251) Chapter 7: Operators on Inner Product Spaces (Page 203-240) Chapter 6: Inner Product Spaces (Page … Continue reading →

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Markov Chain

Posted on May 4, 2015 by Sumant Sumant

Here is a snake and ladder game and this was the markov chain matrix  4.1snakesAndLadders A = [ %1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 W W … Continue reading →

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Clustering Methods in Linear Algebra and finding groupies

Posted on May 2, 2015 by Sumant Sumant

Watch this video What do we do We create adjacency matrix for an undirected graph ie if 1 is connected to 2 then 2 is also connected to 1. We find the diagonal matrix ‘D’ by adding the 1s in … Continue reading →

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Eigen Vector: Shear and Scaling

Posted on April 21, 2015 by Sumant Sumant

The following two matrices Shear Matrix where the angle with which it is sheared. Scaling matrix is  Watch this video

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Pavel Grinfeld’s Linear Algebra 2

Posted on April 14, 2015 by Sumant Sumant

Lecture 18a: Eigen Value decomposition He begins with the matrix  . It’s easy to determine all three eigen values.  As sum of the rows is . One eigen value is and the corresponding eigen vector is . The other eigen value … Continue reading →

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Linear Algebra

Posted on January 19, 2014 by Sumant Sumant

Some of the key ideas in Linear Algebra Matrix Product There are four different ways to look at Matrix-Matrix product Another big idea is to learn about all types of decomposition LU LDU AS = Jordan normal form Singular Value … Continue reading →

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