In‐memory computing (IMC) with crosspoint arrays of resistive switching memory (RRAM) has gained wide attention for accelerating machine learning, data analysis, and deep neural networks. By IMC, matrix‐vector multiplication (MVM) can be executed in the crosspoint array in just one step, thus accelerating a broad range of tasks in machine learning and data analytics. However, a key issue for RRAM crosspoint arrays is the forming operation of the memories which limits the stability and accuracy of the conductance state in the memory device. In this work, a hardware implementation of crosspoint array of forming‐free devices for fast, energy‐efficient accelerators of MVM is reported. RRAM devices with a 1.5 nm‐thick HfO2 layer show an initial low resistance without forming and an analogue‐mode programming behavior for high‐accuracy IMC. Accurate hardware MVM is demonstrated by experimental eigenvalue/eigenvector calculation according to the power‐iteration algorithm, with a fast convergence within about ten iterations to the correct solution. Deflation technique and principal component analysis (PCA) enable the classification of the Iris dataset with 98% accuracy compared with floating‐point implementation. These results support forming‐free crosspoint arrays for accelerating advanced machine learning with IMC.