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If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 … Continue reading
Every real matrix can be decomposed as: where is a orthogonal matrix, is a matrix, having nonzero elements only on the diagonal, and is a orthogonal matrix. We know from the previous post that a symmetric matrix is digonalisable, and … Continue reading
This article involves advanced linear algebra knowledge but it definitely worth understanding it. The previous post contains a proof that a real symmetric matrix has real eigenvalues. Additionally the real symmetric matrices are diagonalizable by an orthogonal matrix. This means: symmetric, … Continue reading
A real matrix is symmetric if . I will show in this post that a real symmetric matrix have real eigenvalues. I will need a dot product for the prof and I’ll use the basic dot product for two vectors … Continue reading
Consider a matrix having lines and columns. The contents of the matrix is filled with 0 or 1 based on the following rules: 1. First line is full of zeros except the central element (position for 0 based index as in C++, … Continue reading
After traveling from a point X on earth 10 km South, 10 km East and 10 km North you arrive at the same location X. Where is X situated? How many such points X exist? The obvious solution is X … Continue reading
Question: You are climbing a stair case. Each time you can either climb 1 stair or 2 stairs. The staircase has n stairs. In how many distinct ways can you climb the staircase ? Answer: There are two possibilities for the … Continue reading