Vector and Space
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Null space and column space basisVector and Space 2021. 6. 23. 15:44
What I want to share in this blog is a basis of null space and column space. 1. a null space and a column space: I told you these in an earlier blog, but I'm going to talk about these again for a quick review. the null space is a set that contains vectors that make an equation a matrix A times a vector x 0. Here it is. column space is a lot easier to understand, which is a set of column vectors ..
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Column space of a matrixVector and Space 2021. 6. 21. 10:24
In this blog, i'm going to talk about column space of a matrix. 1. column space : the column space is all the possible linear combinations of column vectors in a matrix. It definitely contains the 0 vector, is closed under any scalar multiplication and addition. ** Note that a matrix is just a way of writing a set of column vectors. 2. Another way to view it : If Ax is equal to that, and I'm say..
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Null space : Linear IndependenceVector and Space 2021. 6. 3. 15:39
In this blog, i'm going to talk about a null space when column vectors in a matrix are linearly independent. 1. Linear Independence : Before we get into the topic, I want to review the definition of linear independence quickly. The linear independence is vectors in a set that cannot be represented by any linear combination of the other vectors. The null space is a set of vectors that satisfies t..
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Null space of a matrix introductionVector and Space 2021. 5. 31. 21:14
In this chapter, I'm going to talk about null space of a matrix Before we start, Let's review the notions of subspace. 1. What is a subspace ? It's a subset that meets three conditions. The subset contains zero vector. The subset is closed under scalar multiplication. The subset is closed under vector addition. If a subset satisfies the conditions, then we say the subset is a subspace. 2. Null s..
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The multiplication of a matrix vectorVector and Space 2021. 5. 31. 20:44
In this blog, I'm going to deal with the multiplication of a matrix vector. 1. A matrix : it's just an array of numbers. If i have an m by n matrix, the m is the number of rows, and the n is the number of columns. 2. Taking the product of matirx A with some vector x : It only works if the vecotr, x, has the same number of components as A has columns. In other words, if the length of vector x, or..
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Understanding of a functionVector and Space 2021. 1. 1. 10:56
1. A function : A relation between the number of one set and the other set.Or changing a number into another number. Which i drew for helping myself understand the notation of a function. In the photo, i drew a set named X, and the other set named Y. X has two elements to be mapped to two different elements in Y respecticely. So I can say that for any element you give me in the first set(X), I'l..