Computer Science/Linear Algebra 썸네일형 리스트형 04. Subspaces and the basis for a subspace Linear subspaces Subspace of $R \space ^ n$ V is some subsset of vectors, some subset of $R \space ^ n$ . In order for V to be a subspace or a linear subspace of $R \space ^ n$ , This means three things. 📖 Defintion of subspace V contains $\vec {0}$ $\vec {x}$ in V $\longrightarrow$ $c \cdot \vec {x}$ in V (Closure under Multiplication) $\vec {a}, \vec {b}$ in V $\longrightarrow$ $\vec {a} + \ve.. 더보기 03. Linear dependence and independence Linear dependence and independence Ex 1 We call this set linearly dependent set. Linearly dependent means that one of the vector in the set can be represented by some combination of the other vectors in the set. Whichever vector you pick that can be represented by the others, it's not adding any new directionaility or any new information! Ex 2 ❓ Are these linearly independent? ❗ nope! v3 is a .. 더보기 02. Linear combinations and span Linear combination: an expression constructed from a set of terms by multiplying each term by a constant and adding the results. Let's see some examples of linear combinations. There are two vectors which is a=[12] , b=[03] When we scale by some scaling factor and add them, we can get those vectors and it's called a linear combination. ex1) 0⋅a+0⋅b=[00] ✔ zero vector is also a linear combinat.. 더보기 01. Vectors 1. Vector intro for linear algebra Vector has both magnitude and direction. Speed is not a vector. This is considered to be a scalar quantity. If we want it to be a vector, we would also have to specify the direction. Velocity is a vector because it has magnitude and direction. And the interesting thing is that we only care about magnitude & dirrection. We don't necessarily not care where we sta.. 더보기 이전 1 2 다음
