Column Space – The vector space that is spanned by all the C(A) columns in the matrix (A), can also be by row notation written as R(Transpose(A)) If a vector is contained in the column space of a certain matrix, then that vector is a column vector and the coefficients/weights neededContinue Reading
Bayes’ Theorem – Is the probability Event A will happen given (|) Event B happened. P(A|B) = P(B|A) * P(A) / P(B) For example (Assume we have 3 out of 4 probabilities): Calculate a probability that an event A(Eating) will happen given (|) that an event B(Exercising) happened. P(A|B) = P(B|A)Continue Reading
Eigen Decomposition reveals the most important vector in the dataset, the Principal Component (also part of PCA). Eigen Decomposition can be performed only on square matrices. It extracts two features: Eigen Value (a lambda(scaler) that pre multiplies the Eigen Vector) and by reverse the Eigen Vector (a vector which postContinue Reading
Computer machine rounding errors produce values that are close to zero, but are not zero, thus they increase the ranks of a matrix when they shouldn’t. In order to solve this problem a threshold is determined so that the values become zero if they are below the threshold and thusContinue Reading
Matrix Shifting is the action of adding a scalar of the Identity matrix in order to inflate reduced rank matrices so they become full rank which then allows easier work with the matrix. Matrix Shifting has a tradeoff of loss of minimal data. Continue Reading
Frobenius dot product is achieved by computing the hadamard multiplication (elementwise) of two matrices <A,B>with the same dimensionality and summing up all the elements. Another way to achieve the Frobenius dot product is to vectorise(build columnwise: vec(A),vec(B)) both matrices to two vectors with the same size and then perform aContinue Reading
Symboled by a dot in the middle:, and can be done only on two matrices with the same sizes. It’s just as like multiplication of each element with the corresponding element, just like in addition and subtraction. Another thing to know is that Elementwise matrix division is also possible usingContinue Reading
A symmetric matrix is a square matrix that is equal to its transpose. Createing a Symmetric matrix from a square matrix is easy, just add the matrix to it’s transpose and divide by two. Creating a Symmetric matrix from a non square matrix is done by multiplying the matrix withContinue Reading
Applying (pre multiplying) a matrix to a vector gives you either a rotation or a scale(strech/compress) or both a scale(strech/compress) and a rotation. This is called vector transformation, and the (pre multiplying) matrix is called the transformation matrix. No Rotation Case(Pure Scaling ; EigenValue/Eigen Vector) When a vector transformation byContinue Reading
Properties: The result is always a column vector when post multiplying by a vector: A(mXn) * u(nX1) = v(mX1) Taking weighted combinations of the rows of the matrix where the weights are determined by the elements of the vector. result is always a row vector when pre multiplying by aContinue Reading