Suppose a new user’s data that comes in, which is stored in the vector r. Your colleague, a computer scientist, wants to apply an ‘algorithm’ on their ‘computer’ to extract extra information from r. They propose something called ‘deep heart rate parameters’ by solving for z in the problem: r = [H I] z (a) What is the dimensionality of I in this expression. (b) You tell them this idea does not convey any value and is conceptually problematic. Why? Use at most 3 sentences with linear algebraic concepts.
Suppose a new user’s data that comes in, which is stored in the
scientist, wants to apply an ‘algorithm’ on their ‘computer’ to extract extra information from r. They
propose something called ‘deep heart rate parameters’ by solving for z in the problem:
r = [H I] z
(a) What is the dimensionality of I in this expression.
(b) You tell them this idea does not convey any value and is conceptually problematic. Why? Use at most 3 sentences with linear algebraic concepts.
(a) The dimensionality of vector I in the expression r = [H I]z is determined by the number of columns in matrix [H I]. Specifically, it's the number of rows in I, which is equal to the number of columns in [H I].
To clarify further, the expression r = [H I]z suggests that H and I are matrices, where H represents one part of the data, and I represents another part of the data, and z is a vector of parameters. In this context:
- The number of rows in the matrix [H I] is the number of rows in H (assuming both H and I have the same number of rows).
- The number of columns in [H I] is the sum of the number of columns in H and the number of columns in I.
Therefore, the dimensionality of vector I is determined by the number of columns in the matrix [H I], which is the sum of the columns in H and I, not the number of elements in I. My previous explanation was inaccurate, and I apologize for any confusion.
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