Chapter 2 General Vector Spaces
... About the turn of last century, mathematicians noticed that , in the development of both mathematics and its applications, many sets of objects were turning up quite naturally with properties of addition and scalar multiplication in accordance with (A1) through (A7) listed bellow. Moreover, these p ...
... About the turn of last century, mathematicians noticed that , in the development of both mathematics and its applications, many sets of objects were turning up quite naturally with properties of addition and scalar multiplication in accordance with (A1) through (A7) listed bellow. Moreover, these p ...
3. Linear Algebra Review The Range
... since AV1 = 0. Further, the columns of AV2 are linearly independent. To see this, suppose not, that is that there exists a nonzero vector z such that AV2z = 0. Then we would have V2z ∈ null A, which is impossible. Hence the columns of AV2 are a basis for range A, and there are n − dim null A of them ...
... since AV1 = 0. Further, the columns of AV2 are linearly independent. To see this, suppose not, that is that there exists a nonzero vector z such that AV2z = 0. Then we would have V2z ∈ null A, which is impossible. Hence the columns of AV2 are a basis for range A, and there are n − dim null A of them ...
