Outline Recall: For integers Euclidean algorithm for finding gcd’s
... is linearly dependent if there is some linear combination (not with all coefficients ci s being 0) which is the zero vector: 0 = c 1 v1 + c 2 v2 + . . . + c t vt A collection v1 , . . . , vt of vectors is linearly independent if there is no linear combination (except with all coefficients 0) which i ...
... is linearly dependent if there is some linear combination (not with all coefficients ci s being 0) which is the zero vector: 0 = c 1 v1 + c 2 v2 + . . . + c t vt A collection v1 , . . . , vt of vectors is linearly independent if there is no linear combination (except with all coefficients 0) which i ...
Applied Math 9 are two ways to describe a line. If the line is not
... Describe this plane also by a function with x1 and x2 the independent variables, and x3 the dependent variable. 2. A convenient way to describe lines in dimension higher than 2 is also as a set of points. The set ...
... Describe this plane also by a function with x1 and x2 the independent variables, and x3 the dependent variable. 2. A convenient way to describe lines in dimension higher than 2 is also as a set of points. The set ...
Complex Numbers
... Since complex numbers are vectors, expressions such as cz (scaling by a real constant c) or z1+z2 (summation) have the same meaning as in the case of two-dimensional vectors. Clearly, summation of two complex numbers is easiest to perform using Cartesian coordinates (i.e., real and imaginary ...
... Since complex numbers are vectors, expressions such as cz (scaling by a real constant c) or z1+z2 (summation) have the same meaning as in the case of two-dimensional vectors. Clearly, summation of two complex numbers is easiest to perform using Cartesian coordinates (i.e., real and imaginary ...
Lecture 23: Complex numbers Today, we`re going to introduce the
... Today, we’re going to introduce the system of complex numbers. The main motivation for doing this is to establish a somewhat more invariant notion of angle than we have already. Let’s recall a little about how angles work in the Cartesian plane. A brief review of two dimensional analytic geometry Po ...
... Today, we’re going to introduce the system of complex numbers. The main motivation for doing this is to establish a somewhat more invariant notion of angle than we have already. Let’s recall a little about how angles work in the Cartesian plane. A brief review of two dimensional analytic geometry Po ...
Computer modeling of exponential and logarithmic functions of
... The system (30) is a very difficult structure, since it contains the irrationality of the unknown variables, the signs radicands unknown, and exponential functions, in terms of which are the irrationality. Therefore, its solution is generally difficult. However, this type is greatly simplified by fi ...
... The system (30) is a very difficult structure, since it contains the irrationality of the unknown variables, the signs radicands unknown, and exponential functions, in terms of which are the irrationality. Therefore, its solution is generally difficult. However, this type is greatly simplified by fi ...
Dimensions and Vectors
... If we had a world of zero dimensions, there would only be one point. We would not be able to go anywhere. To describe our position, we would not need any number since there would only be one possible location. If we had a world of one dimension (1-D), we could only go forward or backward, not sidewa ...
... If we had a world of zero dimensions, there would only be one point. We would not be able to go anywhere. To describe our position, we would not need any number since there would only be one possible location. If we had a world of one dimension (1-D), we could only go forward or backward, not sidewa ...