### Mathematical Methods Lecture 11 of 34

October 6, 2011 by K.S. Narain

K.S. Narain , ICTP

Here we just upload the videos and now we want to make a summary of what we have done. In the 1st lecture Vector Spaces are argued. All needed definitions of vector in 2 dimensions with length and also with its direction on x,y coordinates were discussed. Adding two vectors was mentioned. The rules of vectors in 2 and 3 dims have been said. Rules of addition and multiplication by numbers and all properties of Null vector have been remarked. Bra-ket notation and negative operator and negative vector discussed. All properties beyond 2 dims mentioned as commutative rule, associative rule, multiplication rule ,associative law for multiplication. Distributive law for addition of numbers and distributive law for addition of vectors are involved.The second lecture was about the expansion of vectors and Matrix equation , more vector notation. The notion of linear dependent ,what kind of transformation is needed for vectors and going from one basis to the other basis. All rules for the scalar product of two vectors are applied. Explaining dual vector space, linear functions or a vector space clarified. The concept of inverse elements, Defining linear vectors and function and the value of the function in terms of basis are regarded. Natural map between vectors is also expressed.

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